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arXiv · 0804.4629

Homotopy shadowing

Yutaka Ishii·John Smillie
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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.

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Yutaka Ishii, John Smillie. 2010-07-23. Homotopy shadowing. https://arxiv.org/abs/0804.4629

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