Pseudo-Anosov maps and continuum theory
Dynamical Systems
2015-09-10 v1
Abstract
In the hyperspace of subcontinua of a compact surface we consider a second order Hausdorff distance. This metric space is compactified in such a way that the stable foliation of a pseudo-Anosov map is naturally identified with a hypercontinuum. We show that negative iterates of a stable arc converges to this hypercontinuum in the considered metric. Some dynamical properties of pseudo-Anosov maps, as topological mixing and the density of stable leaves, are generalized for cw-expansive homeomorphisms of pseudo-Anosov type on compact metric spaces.
Cite
@article{arxiv.1509.02591,
title = {Pseudo-Anosov maps and continuum theory},
author = {Alfonso Artigue},
journal= {arXiv preprint arXiv:1509.02591},
year = {2015}
}