Equidistribution, ergodicity and irreducibility associated with Gibbs measures

  • Adrien Boyer

    The Weizmann Institute of Science, Rehovot, Israel
  • Dustin Mayeda

    The Weizmann Institute of Science, Rehovot, Israel
Equidistribution, ergodicity and irreducibility associated with Gibbs measures cover
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Abstract

We generalize an equidistribution theorem à la Bader–Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in the context of convex cocompact discrete group of isometries of a simply connected connected Riemannian manifold with pinched negative curvature. We combine a functional analytic tool, namely the property RD of hyperbolic groups, together with a dynamical tool: an equidistribution theorem of Paulin, Pollicott and Schapira inspired by a result of Roblin. In particular, we deduce irreducibility of these new classes of boundary representations.

Cite this article

Adrien Boyer, Dustin Mayeda, Equidistribution, ergodicity and irreducibility associated with Gibbs measures. Comment. Math. Helv. 92 (2017), no. 2, pp. 349–387

DOI 10.4171/CMH/414