Equidistribution, ergodicity and irreducibility associated with Gibbs\n measures

2016/01/10 by Adrien Boyer, Boyer, Adrien, Dustin Mayeda +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1601.02275

openalex publication_date 2016/01/10 · openalex created_date 2022/08/06 · openalex updated_date 2026/07/28

Abstract

We generalize an equidistribution theorem `a la Bader-Muchnik for\noperator-valued measures constructed from a family of boundary representations\nassociated with Gibbs measures in the context of convex cocompact discrete\ngroup of isometries of a simply connected connected Riemannian manifold with\npinched negative curvature. We combine a functional analytic tool, namely the\nproperty RD of hyperbolic groups, together with a dynamical tool: an\nequidistribution theorem of Paulin, Pollicott and Schapira inspired by a result\nof Roblin. In particular, we deduce irreducibility of these new classes of\nboundary representations.\n

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