TL;DR
This paper studies expansive homeomorphisms with hyperbolic metrics that exhibit self-similarity, exploring their implications for dimension, entropy, ergodic measures, and transitivity.
Contribution
It introduces the concept of self-similar hyperbolic metrics for expansive homeomorphisms and applies this framework to various dynamical properties.
Findings
Self-similar hyperbolic metrics influence Hausdorff dimension and entropy.
Results on the existence of intrinsically ergodic measures.
Conditions for transitivity in expansive homeomorphisms with canonical coordinates.
Abstract
In this paper we consider expansive homeomorphisms of compact spaces with a hyperbolic metric presenting a self-similar behavior on stable and unstable sets. Several application are given related to Hausdorff dimension, entropy, intrinsically ergodic measures and the transitivity of expansive homeomorphisms with canonical coordinates.
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