Memoirs of the American Mathematical Society 1993; 138 pp; softcover Volume: 103 ISBN10: 0821825534 ISBN13: 9780821825532 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 Order Code: MEMO/103/491
 Let \(F:M\rightarrow M\) denote a selfdiffeomorphism of the smooth manifold \(M\) and let \(\Lambda \subset M\) denote a hyperbolic set for \(F\). Roughly speaking, a Markov cell structure for \(F:M\rightarrow M\) near \(\Lambda\) is a finite cell structure \(C\) for a neighborhood of \(\Lambda\) in \(M\) such that, for each cell \(e \in C\), 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 \(F^{1}\) 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 \(F^q:M\rightarrow M\) has a Markov cell structure near \(\Lambda\). A list of open problems related to Markov cell structures and hyperbolic sets can be found in the final section of the book. Readership Research mathematicians. Table of Contents  Some linear constructions
 Proofs of propositions 2.10 and 2.14
 Some smooth constructions
 The foliation hypothesis
 Smooth triangulation near \(\Lambda\)
 Smooth ball structures near \(\Lambda\)
 Triangulating image balls
 The thickening theorem
 Results in P. L. topology
 Proof of the thickening theorem
 The limit theorem
 Construction of Markov cells
 Removing the foliation hypothesis
 Selected problems
