Joining measures for horocycle flows on abelian covers

2016/07/12 by Wenyu Pan, Pan, Wenyu
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1607.03264

openalex publication_date 2016/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A celebrated result of Ratner from the eighties says that two horocycle flows on hyperbolic surfaces of finite area are either the same up to algebraic change of coordinates, or they have no non-trivial joinings. Recently, Mohammadi and Oh extended Ratner's theorem to horocycle flows on hyperbolic surfaces of infinite area but finite genus. In this paper, we present the first joining classification result of a horocycle flow on a hyperbolic surface of infinite genus: a ℤ or ℤ²-cover of a general compact hyperbolic surface. We also discuss several applications.

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