-
Homotopy shadowing
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 4, August 2010
- pp. 987-1029
- 10.1353/ajm.0.0126
- Article
- Additional Information
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.