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Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups

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arxiv 2404.09718 v2 pith:GLRCYQ6G submitted 2024-04-15 math.DS math.DGmath.GTmath.MG

Pierre-Louis Blayac , Richard Canary , Feng Zhu , Andrew Zimmer This is my paper · ORCID
classification math.DSmath.DGmath.GTmath.MG
keywords anosovassociatedcountingequidistributionfiniteflowgroupsmixing
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We establish counting, mixing and equidistribution results for finite BMS measures on flow spaces associated to geometrically finite convergence group actions. We show that, in particular, these results apply to flow spaces associated to relatively Anosov groups.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classification of horospherical invariant measures in higher rank: The Full Story

    math.DS 2026-01 accept novelty 8.0 of 10

    For Zariski dense Anosov subgroups of arbitrary semisimple real algebraic groups, every horospherical-invariant ergodic Radon measure on the minimal set is a Burger–Roblin measure.

  2. Strict concavity of the growth indicator function for relatively Anosov groups

    math.DG 2026-07 accept novelty 7.0 of 10

    Strict concavity of the growth indicator function is proved for Zariski dense relatively theta-Anosov groups by establishing C^1 regularity of the Manhattan hypersurface.

  3. A geometric correspondence for reparameterizations of geodesic flows

    math.DS 2026-05 unverdicted novelty 7.0 of 10

    Continuous reparameterizations of geodesic flows correspond one-to-one with hyperbolic metric potentials on the fundamental group, with periods matching stable lengths.

  4. Free Semigroups of Large Critical Exponent

    math.GR 2025-02 conditional novelty 7.0 of 10

    For convergence groups with expanding coarse-cocycles, the author builds free subsemigroups with critical exponent arbitrarily close to the ambient critical exponent, with applications to transverse groups and Anosov ...

  5. Regularity of Manhattan manifolds and exact dimensionality for relatively Anosov groups

    math.GR 2026-07 conditional novelty 6.0 of 10

    Relatively Anosov groups have exact-dimensional Patterson–Sullivan measures and C1 Manhattan manifolds, yielding a strictly concave C1 growth indicator.

  6. Orbital counting for relatively Anosov groups

    math.DS 2026-07 conditional novelty 5.0 of 10

    Relatively Anosov subgroups satisfy orbital counting and equidistribution with exponential growth rate e^{δR}, generalizing Sambarino's Anosov theorem.

  7. 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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