Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area - Mathematics > Dynamical SystemsReport as inadecuate




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Abstract: We provide a self-contained, accessible introduction to Ratner-sEquidistribution Theorem in the special case of horocyclic flow on a completehyperbolic surface of finite area. This equidistribution result was firstobtained in the early 1980s by Dani and Smillie and later reappeared as anillustrative special case of Ratner-s work on the equidistribution of unipotentflows in homogeneous spaces. We also prove an interesting probabilistic resultdue to Breuillard: on the modular surface an arbitrary uncentered random walkon the horocycle through almost any point will fail to equidistribute, eventhough the horocycles are themselves equidistributed. In many aspects of thisexposition we are indebted to Bekka and Mayer-s more ambitious survey -ErgodicTheory and Topological Dynamics for Group Actions on Homogeneous Spaces.-



Author: John H. Hubbard, Robyn L. Miller

Source: https://arxiv.org/







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