Homotopy shadowing

Yutaka Ishii, John Smillie

研究成果: Contribution to journalArticle査読

10 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)987-1029
ページ数43
ジャーナルAmerican Journal of Mathematics
132
4
DOI
出版ステータス出版済み - 8 1 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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