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The entropy formula of shrinking target problem in nonautonomous dynamical systems Dyn. Syst. (IF 0.5) Pub Date : 2024-03-27 Yanjie Tang, Xiaojun Lin, Dongkui Ma, Xiaojiang Ye
This paper is devoted to studying the topological entropy of shrinking target problem in nonautonomous dynamical systems (NDSs). After providing the shrinking target problem of the topological vers...
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Global phase portraits of generalized polynomial Liénard system with a unique equilibrium and a periodic annulus Dyn. Syst. (IF 0.5) Pub Date : 2024-03-07 Hebai Chen, Dehong Dai, Zhaosheng Feng
This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types ...
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On the smoothness of principal angles between subspaces and their application to angular values of dynamical systems Dyn. Syst. (IF 0.5) Pub Date : 2024-03-06 Wolf-Jürgen Beyn, Thorsten Hüls
In this work we provide detailed estimates of maximal principal angles between subspaces and we analyse their smoothness for smoothly varying subspaces. This leads to a new definition of angular va...
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Measure-theoretic equicontinuity and rigidity of group actions Dyn. Syst. (IF 0.5) Pub Date : 2024-03-04 Jiandong Yin, Shaoting Xie
Let (G,X) be a G-system, which means that X is a compact Hausdorff space and G is an infinite topological group continuously acting on X, and let μ be a G-invariant measure of (G,X). In this paper,...
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Hausdorff dimension and upper box dimension of a class of homogeneous Moran sets Dyn. Syst. (IF 0.5) Pub Date : 2024-03-04 Shishuang Liu, Yanzhe Li, Wenqi Zong, Chengshuai An
In this paper, we construct a class of special homogeneous Moran sets which is called the {mk}-homogeneous Moran sets by the connected components, and obtain the Hausdorff dimension and the upper b...
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The variational principle of topological r-pressure for amenable group actions Dyn. Syst. (IF 0.5) Pub Date : 2024-02-24 Qiong Wang, Ruifeng Zhang
In this paper, we introduce the notions of the topological r-pressure and measure-theoretic r-pressure for countable discrete amenable group actions. In addition, we establish a variational princip...
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Constrained ergodic optimization for generic continuous functions Dyn. Syst. (IF 0.5) Pub Date : 2024-02-22 Shoya Motonaga, Mao Shinoda
One of the fundamental results of ergodic optimization asserts that for any dynamical system on a compact metric space with the specification property and for a generic continuous function f every ...
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Stability of cycles and survival in a jungle game with four species Dyn. Syst. (IF 0.5) Pub Date : 2024-01-30 Sofia B. S. D. Castro, Ana M. J. Ferreira, Isabel S. Labouriau
The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cyc...
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New classes of C1-robustly transitive maps with persistent critical points Dyn. Syst. (IF 0.5) Pub Date : 2024-01-25 C. Lizana, W. Ranter
Recently, the authors proved in [C. Lizana and W. Ranter, Topological obstructions for robustly transitive endomorphisms on surfaces, Adv. Math. 390 (2021), pp. 107901] that every C1-robustly trans...
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Asymptotically autonomous stability of kernel sections for lattice plate equations with nonlinear damping Dyn. Syst. (IF 0.5) Pub Date : 2024-01-23 Mirelson M. Freitas, Anderson J. A. Ramos, Jociane S. Fonseca
We develop the theory of kernel sections of non-autonomous dynamical systems. Under some sufficient conditions, we establish some abstract results on the asymptotically autonomous stability of kern...
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Stochastic travelling wave of three-species competitive–cooperative systems with multiplicative noise Dyn. Syst. (IF 0.5) Pub Date : 2023-12-28 Hao Wen, Jianhua Huang, Liang Zhang
This paper is devoted to the stochastic travelling wave solutions of a three-species competitive–cooperative system with multiplicative noise. The existence of the travelling wave solutions can be ...
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Homoclinic points of symplectic partially hyperbolic systems with 2D centre Dyn. Syst. (IF 0.5) Pub Date : 2023-12-27 Pengfei Zhang
We consider a generic symplectic partially hyperbolic diffeomorphism close to direct/skew products of symplectic Anosov diffeomorphisms with area-preserving diffeomorphisms and prove that every hyp...
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Centralizer of fixed point free separating flows Dyn. Syst. (IF 0.5) Pub Date : 2023-12-05 Bo Han, Xiao Wen
In this paper, we study the centralizer of a separating continuous flow without fixed points. We show that if M is a compact metric space and ϕt:M→M is a separating flow without fixed points, then ...
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Novel regularized dynamical systems for solving hierarchical fixed point problems Dyn. Syst. (IF 0.5) Pub Date : 2023-11-27 Trinh Ngoc Hai
In this paper, we study some Krasnoselskii-Mann type dynamical systems in solving fixed point problems. The first one can be regarded as a continuous version of the Krasnoselskii-Mann iterations. W...
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On real center singularities of complex vector fields on surfaces Dyn. Syst. (IF 0.5) Pub Date : 2023-10-25 V. León, B. Scárdua
One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral...
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The generalized IFS Bayesian method and an associated variational principle covering the classical and dynamical cases Dyn. Syst. (IF 0.5) Pub Date : 2023-09-18 Artur O. Lopes, Jairo. K. Mengue
We introduce a general IFS Bayesian method for getting posterior probabilities from prior probabilities, and also a generalized Bayes' rule, which will contemplate a dynamical, as well as a non-dyn...
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Conditional Brin-Katok's entropy formula for monotonic partitions on Feldman-Katok metric Dyn. Syst. (IF 0.5) Pub Date : 2023-09-09 Xiaona Fang, Ran Lu
In this paper, we build the Brin-Katok's formula of conditional entropy with respect to invariant, decreasing and a large family of increasing measurable partitions by replacing the Bowen metric with the Feldman-Katok metric.
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On the distality and expansivity of certain maps on spheres Dyn. Syst. (IF 0.5) Pub Date : 2023-09-03 Manoj Choudhuri, Gianluca Faraco, Alok Kumar Yadav
Any affine map on the (n + 1)-dimensional Euclidean space gives rise to a natural map on the n-dimensional sphere whose dynamical aspects are not so well-studied in the literature. We explore the d...
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Discrete spectrum for group actions Dyn. Syst. (IF 0.5) Pub Date : 2023-07-21 Fang Xu, Leiye Xu
In this paper, we study discrete spectrum of invariant measures for group actions. We show that an invariant measure has discrete spectrum if and only if it has finite max-mean-measure-complexity. ...
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Weaker forms of specification for maps on uniform spaces Dyn. Syst. (IF 0.5) Pub Date : 2023-07-18 Naveenkumar Yadav
We introduce and study here some weaker forms of specification property for uniformly continuous surjective self-maps on uniform spaces, namely topological quasi-weak specification property, topolo...
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Cramér distance and discretizations of circle expanding maps II: simulations Dyn. Syst. (IF 0.5) Pub Date : 2023-07-16 Pierre-Antoine Guihéneuf, Maurizio Monge
This paper presents some numerical experiments in relation with the theoretical study of the ergodic short-term behaviour of discretizations of expanding maps done in P.-A. Guihéneuf and M. Monge, ...
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Long-time behaviour of solutions of superlinear systems of differential equations Dyn. Syst. (IF 0.5) Pub Date : 2023-07-14 Luan Hoang
This paper establishes the precise asymptotic behaviour, as time t tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowes...
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Reversible global centres with quintic homogeneous nonlinearities Dyn. Syst. (IF 0.5) Pub Date : 2023-07-10 Jaume Llibre, Claudia Valls
A centre of a differential system in the plane R2 is a singular point p having a neighbourhood U such that U∖{p} is filled of periodic orbits. A global centre is a centre p such that R2∖{p} is...
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Existence of SRB measures for hyperbolic maps with weak regularity Dyn. Syst. (IF 0.5) Pub Date : 2023-07-04 Houssam Boukhecham
We prove that a C1 hyperbolic map whose differential is regular enough has an SRB measure. The precise regularity condition is weaker than Hölder and was mentioned by various authors through the d...
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A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages Dyn. Syst. (IF 0.5) Pub Date : 2023-07-03 Sohail Farhangi
We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between sequences of vecto...
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Topological pressure for conservative C1-diffeomorphisms with no dominated splitting Dyn. Syst. (IF 0.5) Pub Date : 2023-07-03 Xueming Hui
We prove three formulas for computing the topological pressure of C1-generic conservative diffeomorphism with no dominated splitting and show the continuity of topological pressure with respect to...
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A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature Dyn. Syst. (IF 0.5) Pub Date : 2023-06-28 Keith Burns, Dong Chen
For any rank 1 nonpositively curved surface M, it was proved by Burns-Climenhaga-Fisher-Thompson that for any q<1, there exists a unique equilibrium state μq for qφu, where φu is the geometric...
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(X,Y,φ)-Stable semigroups, periodic solutions, and applications Dyn. Syst. (IF 0.5) Pub Date : 2023-06-26 Thieu Huy Nguyen, Thi Ngoc Ha Vu, Thi Kim Oanh Tran
Motivated by the Lp−Lq smoothing properties of heat semigroups on unbounded domains and the conditional stability of hyperbolic semigroups, we develop a unified approach toward the problems on the...
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Topological stability and pseudo-orbit tracing property of Borel measures from the viewpoint of open covers Dyn. Syst. (IF 0.5) Pub Date : 2023-06-23 Shuzhen Hua, Jiandong Yin
In the paper, we introduce the concepts of topological stability, expansivity and pseudo-orbit tracing property of Borel measures with respect to a given continuous map on a compact topological spa...
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A note on the marginal instability rates of two-dimensional linear cocycles Dyn. Syst. (IF 0.5) Pub Date : 2023-06-21 Ian D. Morris, Jonah Varney
A theorem of Guglielmi and Zennaro implies that if the uniform norm growth of a locally constant GL2(R)-cocycle on the full shift is not exponential, then it must be either bounded or linear, with...
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Behaviour of trajectories near a two-cycle heteroclinic network Dyn. Syst. (IF 0.5) Pub Date : 2023-06-19 Olga Podvigina
Heteroclinic networks and cycles are invariant sets comprised of interacting nodes connected by heteroclinic trajectories. Often the sets are not asymptotically stable but attract a positive measur...
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Differentiability of the largest Lyapunov exponent for planar open billiards Dyn. Syst. (IF 0.5) Pub Date : 2023-06-07 Amal Al Dowais
In this paper, we estimate the largest Lyapunov exponent for open billiards in the plane. We show that the largest Lyapunov exponent is differentiable with respect to a billiard deformation.
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One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz–Krieger algebras Dyn. Syst. (IF 0.5) Pub Date : 2023-05-30 Kengo Matsumoto
We will characterize topologically conjugate one-sided topological Markov shifts in terms of their subgroups of continuous full groups and subalgebras of Cuntz–Krieger algebras.
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Hausdorff and packing dimensions of homogeneous product Moran sets Dyn. Syst. (IF 0.5) Pub Date : 2023-05-10 Qi Wang
Let M({ns},{ms},{cs},{ds}) be the collection of homogeneous product Moran sets determined by two sequences of positive integers {ns}, {ms} and two sequences of positive numbers {cs}, {ds}. We obtain the maximal and minimal values of the Hausdorff and packing dimensions of elements in M.
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A prey–predator model with three interacting species Dyn. Syst. (IF 0.5) Pub Date : 2023-05-09 U.U. Jamilov, M. Scheutzow, I. Vorkastner
We consider a class of discrete time prey–predator models with three interacting species defined on the two-dimensional simplex. For some choices of parameters of the operator describing the evolut...
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Sensitivity, local stable/unstable sets and shadowing Dyn. Syst. (IF 0.5) Pub Date : 2023-05-09 Mayara Antunes, Bernardo Carvalho, Margoth Tacuri
In this paper, we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary, we generalize results in [Artigue et al. Beyond topological hyperbolicity: the Lshadowing property, J. Differ. Equ. 268(6) (2020), pp. 3057–3080
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The 0:1 resonance bifurcation associated with the supercritical Hamiltonian pitchfork bifurcation Dyn. Syst. (IF 0.5) Pub Date : 2023-04-09 Xing Zhou
We consider the non-semisimple 0:1 resonance (i.e. the unperturbed equilibrium has two purely imaginary eigenvalues ±iα±iα ( α∈R and α>0) and a non-semisimple double-zero one) Hamiltonian bifurcation with one distinguished parameter, which corresponds to the supercritical Hamiltonian pitchfork bifurcation. Based on BCKV singularity theory established by [H.W. Broer, S. -N. Chow, Y. Kim, and G. Vegter
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Structure and dimension of invariant subsets of expanding Markov maps and joint invariance Dyn. Syst. (IF 0.5) Pub Date : 2023-04-09 Georgios Lamprinakis
A long-standing question is what invariant subsets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved maps are commuting the answer is almost complete. However very little is known in the non-commutative case. A first step is to analyse the structure of the invariant
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On the dynamics of the combinatorial model of the real line Dyn. Syst. (IF 0.5) Pub Date : 2023-04-09 Pedro J. Chocano
We study dynamical systems defined on the combinatorial model of the real line. We prove that using single-valued maps there are no periodic points of period 3, which contrasts with the classical and less restrictive setting. Then, we use Vietoris-like multivalued maps to show that there is more flexibility, at least in terms of periods, in this combinatorial framework than in the usual one because
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Dynamics of stochastic FitzHugh–Nagumo system on unbounded domains with memory Dyn. Syst. (IF 0.5) Pub Date : 2023-04-04 Bui Kim My, Nguyen Duong Toan
In this paper, we consider the non-autonomous stochastic FitzHugh–Nagumo system with hereditary memory and a very large class of nonlinearities, which has no restriction on the upper growth of the nonlinearity. The existence of a random pullback attractor is established for this system in all N-dimensional space.
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Upper semicontinuity of the global attractor for Bresse system with second sound Dyn. Syst. (IF 0.5) Pub Date : 2023-04-04 M. M. Freitas, A. J. A. Ramos, M. Aouadi, D. S. Almeida Júnior
In this paper, we study the long-time dynamics of Bresse system under mixed homogeneous Dirichlet–Neumann boundary conditions. The heat conduction is given by Cattaneo's law. Only the shear angle displacement is damped via the dissipation from the Cattaneo's law, and the vertical displacement and the longitudinal displacement are free. Under quite general assumptions on the source term and based on
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Cross-sections to flows and intrinsically harmonic forms Dyn. Syst. (IF 0.5) Pub Date : 2023-03-26 Slobodan N. Simić
We establish a new criterion for the existence of a global cross-section to non-singular volume-preserving flows on compact manifolds. Namely, we show that if Φ is a non-singular smooth flow on a compact, connected manifold M with a smooth invariant volume form Ω, then Φ admits a global cross-section if and only if the (n−1)-form iXΩ is intrinsically harmonic, that is, harmonic with respect to some
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Continuity of isomorphisms applied to rigidity problems of entropy spectra Dyn. Syst. (IF 0.5) Pub Date : 2023-03-26 Katsukuni Nakagawa
For a fixed topological Markov shift, we consider measure-preserving dynamical systems of Gibbs measures for 2-locally constant functions on the shift. We also consider isomorphisms between two such systems. We study the set of all 2-locally constant functions f on the shift such that all those isomorphisms defined on the system associated with f are induced from automorphisms of the shift. We prove
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Correction Dyn. Syst. (IF 0.5) Pub Date : 2023-03-18
Published in Dynamical Systems: An International Journal (Vol. 38, No. 3, 2023)
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Non-rigid rank-one infinite measures on the circle Dyn. Syst. (IF 0.5) Pub Date : 2023-03-18 Hindy Drillick, Alonso Espinosa-Dominguez, Jennifer N. Jones-Baro, James Leng, Yelena Mandelshtam, Cesar E. Silva
For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing and classify when the measure is finite or infinite. In the finite case they are isomorphic to irrational rotations, giving explicit rank-one cutting and spacer parameters for these irrational rotations. In the infinite case we use
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Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps Dyn. Syst. (IF 0.5) Pub Date : 2023-03-16 Na Yuan, Bing Li
Let T be an expanding Markov map with a repeller E defined on X⊂[0,1]. This paper concerns the Hausdorff dimension of the sets {x∈X:|Tnx−gn(x)|
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Topological pressure of a factor map for nonautonomous dynamical systems Dyn. Syst. (IF 0.5) Pub Date : 2023-03-15 Lei Liu, Cao Zhao
Let (X,d)(X,d) be a compact metric space and {fi}∞i=1{fi}i=1∞ be a sequence of continuous maps from X to itself. Denote by f1,∞f1,∞ the sequence {fi}∞i=1 and by (X,d,f1,∞) the induced nonautonomous dynamical system. In this paper, we give the definitions of upper capacity topological pressure and Pesin-Pitskel topological pressure on a noncompact subset for nonautonomous dynamical systems from the
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Bratteli diagrams for bounded topological speedups Dyn. Syst. (IF 0.5) Pub Date : 2023-02-19 Drew D. Ash, Andrew Dykstra, Michelle LeMasurier
ABSTRACT A bounded topological speedup of a Cantor minimal system (X,T) is a minimal system (X,S), where S(x)=Tp(x)(x) for some bounded function p:X→Z+, or any system topologically conjugate to such an (X,S). Assuming the system (X,T) is represented by a properly ordered Bratteli diagram B, we provide a method for constructing a new, perfectly ordered Bratteli diagram B~ that represents the sped-up
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Thomae's function and the space of ergodic measures Dyn. Syst. (IF 0.5) Pub Date : 2023-02-19 Anton Gorodetski, Alexandro Luna
We study the space of ergodic measures of the map f:T2→T2,f(x,y)=(x,x+y)(mod1),and show that its structure is similar to the graph of Thomae's function.
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Ordinary differential equations defined by a trigonometric polynomial field: behaviour of the solutions Dyn. Syst. (IF 0.5) Pub Date : 2023-02-19 W. Oukil
ABSTRACT We consider the ordinary differential equations defined by a trigonometric polynomial field and we prove that any solution x admits a rotation vector ρ∈Rn. More precisely, the function t↦x(t)−ρt is bounded on time and it is a weak almost periodic function of slope ρ.
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On codimension one special Anosov endomorphisms Dyn. Syst. (IF 0.5) Pub Date : 2023-02-05 Xiang Zhang
We show that if a closed smooth n-manifold M admits a u-dimension one special Anosov endomorphism f, then M is homeomorphic to Tn and f is topologically conjugate to a hyperbolic toral endomorphism. Moreover, any u-dimension one special Anosov endomorphism is transitive and the stable foliation is minimal.
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On calculation of the exact Lyapunov exponent of affine Boole transformations Dyn. Syst. (IF 0.5) Pub Date : 2023-02-05 Mátyás Barczy
We show an elementary way to calculate the exact Lyapunov exponent of affine Boole transformations using the interchangeability theorem for differentiation and integration due to Leibniz.
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Nonuniform contractions and converse stability results via a smooth topological equivalence Dyn. Syst. (IF 0.5) Pub Date : 2023-01-22 Álvaro Castañeda, Pablo Monzón, Gonzalo Robledo
Given a nonautonomous linear system of ordinary differential equations with nonuniform contractions on the half line, we study the smoothness and preserving orientation properties of a global linearization between this system and a family of nonlinear perturbations. As an application of the previous study, we improve a converse stability result for the nonlinear system in terms of density functions
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Two-dimensional heteroclinic connections in the generalized Lotka–Volterra system Dyn. Syst. (IF 0.5) Pub Date : 2023-01-12 Olga Podvigina
We consider a three-dimensional generalized Lotka–Volterra (GLV) system assuming that it has equilibria on each of the coordinate axes, stable along the respective directions, and heteroclinic trajectories, ξ1→ξ2 and ξ1→ξ3, that belong to coordinate planes. For such a system we give a complete classification of possible types of dynamics, characterized by the existence or non-existence of various two-dimensional
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A computer-assisted proof of dynamo growth in the stretch-fold-shear map Dyn. Syst. (IF 0.5) Pub Date : 2022-12-17 F. A. Pramy, B. D. Mestel, A. D. Gilbert
The Stretch-Fold-Shear (SFS) operator Sα is a functional linear operator acting on complex-valued functions of a real variable x on some domain containing [−1,1] in R. It arises from a stylized model in kinematic dynamo theory where magnetic field growth corresponds to an eigenvalue of modulus greater than 1. When the shear parameter α is zero, the spectrum of Sα can be determined exactly, and the
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Statistical solution and Liouville-type theorem for the nonautonomous discrete Selkov model Dyn. Syst. (IF 0.5) Pub Date : 2022-11-28 Congcong Li, Chunqiu Li, Jintao Wang
In this article, we study the statistical solution of the nonautonomous discrete Selkov model. First, we show the existence of a pullback- D attractor for the system and establish the existence of a unique family of invariant Borel probability measures carried by the pullback- D attractor. Then we further prove that the family of invariant Borel probability measures is a statistical solution for the
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Global attractor for a degenerate Klein–Gordon–Schrödinger-type system Dyn. Syst. (IF 0.5) Pub Date : 2022-11-17 M. N. Poulou, N. B. Zographopoulos
In this paper, we study the long-time behaviour of solutions of a degenerate Klein–Gordon–Schrödinger-type system which is defined in a bounded domain. First, we proved the existence, uniqueness and continuity of the solutions on the initial data, then the asymptotic compactness of the solutions and finally the existence of a global compact attractor.
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Effect of noise on residence times of a heteroclinic cycle Dyn. Syst. (IF 0.5) Pub Date : 2022-10-30 Valerie Jeong, Claire Postlethwaite
A heteroclinic cycle is an invariant set in a dynamical system consisting of saddle-type equilibria and heteroclinic connections between them. It is known that deterministic perturbations (inputs) to a heteroclinic cycle generally lead to periodic solutions. Addition of noise to such a system leads to a non-intuitive result: there is a range of noise levels for which the mean residence time near the
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A topological characterization of periodic flows Dyn. Syst. (IF 0.5) Pub Date : 2022-10-30 Khadija Ben Rejeb
Let G={ht|t∈R} be a continuous flow of homeomorphisms of a connected n-manifold M. The flow G is called periodic if: for some real s>0, hs=identity. A global section for a flow G is a closed subset K of M such that every orbit under G intersects K in exactly one point. In this paper, we give a topological characterization of periodic flows with global sections for M=Rn. Next, we consider periodic flows
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Piecewise rotations: limit set for the non-bijective maps Dyn. Syst. (IF 0.5) Pub Date : 2022-10-24 Nicolas Bédaride, Jean-François Bertazzon, Idrissa Kaboré
We consider non-bijective piecewise rotations of the plane. These maps belong to a family introduced in previous papers by Boshernitzan and Goetz. We derive in this paper some upper bounds to the size of the limit set. This improves results of [M. Boshernitzan and A. Goetz, A dichotomy for a two-parameter piecewise rotation, Ergodic Theory Dynam. Syst. 23(3) (2003), pp. 759–770.].