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.