Markov Cell Structures Near a Hyperbolic Set (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Hardcover

Farrell, F. Thomas; Jones, Lowell

Hardcover

ISBN 10: 0821825534 ISBN 13: 9780821825532

Publisher: American Mathematical Society, 1993

Synopsis

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.

About this title

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• Language: English
• ISBN 10: 0821825534
• ISBN 13: 9780821825532
• Binding: Hardcover
• Number of pages: 138