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Emergence of Strange Attractors from Singularities

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Abstract

This paper is a summary of results that prove the abundance of one-dimensional strange attractors near a Shil’nikov configuration, as well as the presence of these configurations in generic unfoldings of singularities in \(\mathbb{R}^{3}\) of minimal codimension. Finding these singularities in families of vector fields is analytically possible and thus provides a tractable criterion for the existence of chaotic dynamics. Alternative scenarios for the possible abundance of two-dimensional attractors in higher dimension are also presented. The role of Shil’nikov configuration is now played by a certain type of generalised tangency which should occur for families of vector fields \(X_{\mu}\) unfolding generically some low codimension singularity in \(\mathbb{R}^{n}\) with \(n\geqslant 4\).

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  • 29 October 2023

    The numbering issue has been changed to 4-5.

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During the preparation of this paper, the author was supported by Spanish Research project PID2020-113052GB-I00.

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  1. Departamento de Matemáticas, Universidad de Oviedo, c/ Leopoldo Calvo Sotelo 18, 33007, Oviedo, Spain

    José Angel Rodríguez

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34C23, 37D05, 37D25, 37D45, 37G05, 37G10, 37G25

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Rodríguez, J.A. Emergence of Strange Attractors from Singularities. Regul. Chaot. Dyn. 28, 468–497 (2023). https://doi.org/10.1134/S1560354723520040

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