Markov cell structures near a hyperbolic set / Tom Farrell, Lowell Jones.

Format:

Book

Author/Creator:

Farrell, F. Thomas, 1941- author.

Jones, Lowell, 1945- author.

Series:

Memoirs of the American Mathematical Society ; Volume 103, Number 491.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 103, Number 491

Language:

English

Subjects (All):

Diffeomorphisms.

Manifolds (Mathematics).

Hyperbolic spaces.

Physical Description:

1 online resource (151 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island, United States : American Mathematical Society, 1993.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""1. Introduction""; ""2. Some Linear Constructions""; ""3. Proofs of Propositions 2.10 and 2.14""; ""4. Some Smooth Constructions""; ""5. The Foliation Hypothesis""; ""6. Smooth Triangulation Near Î?""; ""7. Smooth Ball Structures Near Î?""; ""8. Triangulating Image Balls""; ""9. The Thickening Theorem""; ""10. Results in P.L. Topology""; ""11. Proof of the Thickening Theorem""; ""12. The Limit Theorem""; ""13. Construction of Markov Cells""; ""14. Removing the Foliation Hypothesis""; ""15. Selected Problems""; ""References""

Notes:

"May 1993, Volume 103, Number 491 (second of 4 numbers)"--Cover.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0068-5