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Creators/Authors contains: "CANARY, RICHARD"

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  1. ; ; (, Mathematische Annalen)
    Free, publicly-accessible full text available June 1, 2026
  2. ; ; (, Journal of Modern Dynamics)
    Forni, Giovanni (Ed.)
    We study Patterson–Sullivan measures for a class of discrete subgroups of higher rank semisimple Lie groups, called transverse groups, whose limit set is well-defined and transverse in a partial flag variety. This class of groups includes both Anosov and relatively Anosov groups, as well as all discrete subgroups of rank one Lie groups. We prove an analogue of the Hopf–Tsuji–Sullivan dichotomy and then use this dichotomy to prove a variant of Burger's Manhattan Curve Theorem. We also use the Patterson–Sullivan measures to obtain conditions for when a subgroup has critical exponent strictly less than the original transverse group. These gap results are new even for Anosov groups. 
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  3. ; ; ; (, Advances in Mathematics)
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  4. ; ; (, Algebraic & Geometric Topology)
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  5. ; ; (, Advances in Mathematics)
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  6. ; ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We show that if an eventually positive, non-arithmetic, locally Hölder continuous potential for a topologically mixingcountable Markov shift with (BIP) has an entropy gap at infinity,then one may apply the renewal theorem of Kesseböhmer and Kombrink to obtain counting and equidistributionresults. We apply these general results to obtain counting and equidistribution results for cusped Hitchinrepresentations, and more generally for cusped Anosov representations of geometrically finite Fuchsian groups. 
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  7. (, EMS Surveys in Mathematical Sciences)
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  8. ; ; (, Advances in Mathematics)
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  9. ; ; (, Ergodic Theory and Dynamical Systems)
    We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space of a closed orientable surface of genus at least 2, then we explain the construction for Hitchin components and finally we treat the general case. This paper surveys results of Bridgeman, Canary, Labourie and Sambarino, The pressure metric for Anosov representations , and discusses questions and open problems which arise. 
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  10. ; (, Journal of Topology)