AMS Bookstore LOGO amslogo
Return to List  Item: 1 of 1   
Markov Cell Structures near a Hyperbolic Set
Tom Farrell and Lowell Jones

Memoirs of the American Mathematical Society
1993; 138 pp; softcover
Volume: 103
ISBN-10: 0-8218-2553-4
ISBN-13: 978-0-8218-2553-2
List Price: US$40
Individual Members: US$24
Institutional Members: US$32
Order Code: MEMO/103/491
[Add Item]

Request Permissions

Let \(F:M\rightarrow M\) denote a self-diffeomorphism 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.


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
Powered by MathJax
Return to List  Item: 1 of 1   

  AMS Home | Comments:
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia