Markov cell structures near a hyperbolic set
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Bibliographic Information
Markov cell structures near a hyperbolic set
（Memoirs of the American Mathematical Society, no. 491）
American Mathematical Society, 1993
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"May 1993, volume 103, number 491 (second of 4 numbers)"--T.p
Includes bibliographical references
Description and Table of Contents
Description
Let F: M - M denote a self-diffeomorphism of the smooth manifold M and let *L M denote a hyperbolic set for F . Roughly speaking, a Markov cell structure for F: M M near *L is a finite cell structure C for a neighbourhood of *L in M such that, for each cell *e *E C, the image under F of the unstable factor of *e is equal to the union of the unstable factors of a subset of C, and the image of the stable factor of *e under F ]x1 is equal to the union of the stable factors of a subset of C . The main result of this work is that for some positive integer q, the diffeomorphism F ]xq: M - M has a Markov cell structure near *L. A list of open problems related to Markov cell structures and hyperbolic sets can be found in the final section of the book.
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