Abstract
Let G be a connected, real linear, semisimple Lie group without compact factors and Γ < G a Zariski dense, discrete subgroup. We study the topological dynamics of positive diagonal flows on ΓG. We extend Hopf coordinates to Bruhat–Hopf coordinates of G, which gives the framework to estimate the elliptic part of products of large generic loxodromic elements. By rewriting results of Guivarc’h–Raugi into Bruhat–Hopf coordinates, we partition the preimage in ΓG of the non-wandering set of mixing regular Weyl chamber flows, into finitely many dynamically conjugated subsets. We prove a necessary condition for topological mixing, and when the connected component of the identity of the centralizer of the Cartan subgroup is abelian, we prove it is sufficient.
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Acknowledgments
The author acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—281869850 (RTG 2229). She would like to thank O. Glorieux, B. Pozzetti, her PhD advisors F. Maucourant and B. Schapira for encouragements, fruitful discussions and comments and lastly, the referee for their remarks and suggestions to improve the paper and pointing out that the paper needed an index.
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Dang, NT. Topological mixing of positive diagonal flows. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2561-1
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DOI: https://doi.org/10.1007/s11856-023-2561-1