Patterson-Sullivan measures for relatively Anosov groups
Richard Canary, Andrew Zimmer, Tengren Zhang
TL;DR
This paper develops Patterson-Sullivan measures for relatively Anosov groups, proving their existence, uniqueness, and ergodicity, and applies these results to entropy gap and concavity theorems.
Contribution
It introduces the first comprehensive theory of Patterson-Sullivan measures for relatively Anosov groups, including key properties and applications.
Findings
Existence and uniqueness of Patterson-Sullivan measures for relatively Anosov groups
Ergodicity of these measures
Entropy gap and strict entropy concavity results
Abstract
We establish existence, uniqueness and ergodicity results for Patterson-Sullivan measures for relatively Anosov groups. As applications we obtain an entropy gap theorem and a strict concavity result for entropies associated to linear functionals.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Topological and Geometric Data Analysis