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TOPOLOGICAL MIXING OF POSITIVE DIAGONAL FLOWS

Abstract : Let G be a semi-simple real Lie group without compact factors and Γ < G a Zariski dense, discrete subgroup. We study the topological dynamics of positive diagonal flows on Γ\G. 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 Γ\G 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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https://hal.archives-ouvertes.fr/hal-03010830
Contributor : Nguyen-Thi Dang Connect in order to contact the contributor
Submitted on : Wednesday, November 25, 2020 - 6:51:39 PM
Last modification on : Thursday, December 10, 2020 - 3:06:23 AM

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  • HAL Id : hal-03010830, version 2

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Nguyen-Thi Dang. TOPOLOGICAL MIXING OF POSITIVE DIAGONAL FLOWS. 2020. ⟨hal-03010830v2⟩

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