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Patterson-Sullivan measures for relatively Anosov groups

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arxiv 2308.04023 v4 pith:ITT7BEVT submitted 2023-08-08 math.DS math.GR

Richard Canary , Andrew Zimmer , Tengren Zhang This is my paper · ORCID
classification math.DSmath.GR
keywords anosovgroupsmeasurespatterson-sullivanrelativelyapplicationsassociatedconcavity
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We establish existence, uniqueness and ergodicity results for Patterson-Sullivan measures for relatively Anosov groups. As applications we obtain an entropy gap theorem and a strict concavity result for entropies associated to linear functionals.

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  1. Geometry and Dynamics of Transverse Groups

    math.DS 2025-02 conditional

    A survey of recent work showing that Patterson-Sullivan theory, including shadow lemmas and the Hopf-Tsuji-Sullivan dichotomy, extends to transverse subgroups of SL(d,R), with applications to Anosov and relatively Ano...

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