Homotopy shadowing
Dynamical Systems
2010-07-26 v2
Abstract
Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we consider certain expanding maps on metric spaces. In a second direction we consider maps which are hyperbolic with respect to product cone fields on a product manifold. A key step in the proof is to establish a shadowing theorem for pseudo--orbits with some additional homotopy information.
Cite
@article{arxiv.0804.4629,
title = {Homotopy shadowing},
author = {Yutaka Ishii and John Smillie},
journal= {arXiv preprint arXiv:0804.4629},
year = {2010}
}
Comments
42 pages, 17 figures. This version contains a corrected proof of Proposition 5.11