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

2019/11/18 by Shwartz, Ofer
#20F67 #30F35 #31C35 #37D40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.07797

Abstract

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.

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