Markov Cell Structures Near a Hyperbolic Set

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.Farrell, Tom is the author of 'Markov Cell Structures Near a Hyperbolic Set' with ISBN 9780821825532 and ISBN 0821825534.