The orbital counting problem for hyperconvex representations

DOI10.5802/aif.2973zbMath1354.22016arXiv1203.0280OpenAlexW2964222195MaRDI QIDQ5962682

Andrés Sambarino

Publication date: 15 February 2016

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0280

zbMATH Keywords

Lie groupsmixingcounting problemhigher rank geometriesHitchin representationshyperconvex representations

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Related Items (21)

Patterson–Sullivan theory for Anosov subgroups ⋮ Fourier decay, renewal theorem and spectral gaps for random walks on split semisimple Lie groups ⋮ An introduction to pressure metrics for higher Teichmüller spaces ⋮ Counting problems for special-orthogonal Anosov representations ⋮ Eigenvalues and entropy of a Hitchin representation ⋮ Anosov groups: local mixing, counting and equidistribution ⋮ Ergodicity and equidistribution in Hilbert geometry ⋮ Anosov representations with Lipschitz limit set ⋮ A report on an ergodic dichotomy ⋮ Hitchin representations of Fuchsian groups ⋮ Geodesic coordinates for the pressure metric at the Fuchsian locus ⋮ The Hopf-Tsuji-Sullivan dichotomy in higher rank and applications to Anosov subgroups ⋮ Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds ⋮ Correlation of the renormalized Hilbert length for convex projective surfaces ⋮ Torus counting and self-joinings of Kleinian groups ⋮ Topological mixing of Weyl chamber flows ⋮ Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds ⋮ Quantitative properties of convex representations ⋮ Cross ratios on boundaries of symmetric spaces and euclidean buildings ⋮ Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations ⋮ On the hyperbolic orbital counting problem in conjugacy classes

Cites Work

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• Quantitative properties of convex representations
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• Hyperconvex representations and exponential growth
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