Homotopy shadowing

Yutaka Ishii, John Smillie

    Research output: Contribution to journalArticlepeer-review

    13 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 2010

    All Science Journal Classification (ASJC) codes

    • General Mathematics


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