Homotopy shadowing

Yutaka Ishii, John Smillie

Research output: Contribution to journalArticle

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)987-1029
Number of pages43
JournalAmerican Journal of Mathematics
Issue number4
Publication statusPublished - Aug 1 2010


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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