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1 results

  • The conformal measures of a normal subgroup of a cocompact Fuchsian group

  • Part of
  • OFER SHWARTZ
  • Journal:
    Ergodic Theory and Dynamical Systems / Volume 41 / Issue 9 / September 2021
    Published online by Cambridge University Press:
    28 September 2020, pp. 2845-2878
    Print publication:
    September 2021
    • Article
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  • In this paper we study the conformal measures of a normal subgroup of a cocompact Fuchsian group. In particular, we relate the extremal conformal measures to the eigenmeasures of a suitable Ruelle operator. Using Ancona’s theorem, adapted to the Ruelle operator setting, we show that if the group of deck transformations G is hyperbolic then the extremal conformal measures and the hyperbolic boundary of G coincide. We then interpret these results in terms of the asymptotic behavior of cutting sequences of geodesics on a regular cover of a compact hyperbolic surface.