Global Stability of Dynamical Systems

1. Front Matter

   Pages i-xii

   PDF

2. Generalities

   • Michael Shub

   Pages 1-7

3. Filtrations

   • Michael Shub

   Pages 8-12

4. Sequences of Filtrations

   • Michael Shub

   Pages 13-19

5. Hyperbolic Sets

   • Michael Shub

   Pages 20-32

6. Stable Manifolds

   • Michael Shub

   Pages 33-70

7. Stable Manifolds for Hyperbolic Sets

   • Michael Shub

   Pages 71-82

8. More Consequences of Hyperbolicity

   • Michael Shub

   Pages 83-99

9. Stability

   • Michael Shub

   Pages 100-116

10. A Potpourri of Stability Results

    • Michael Shub

    Pages 117-121

11. Markov Partitions

    • Michael Shub

    Pages 122-146

12. Back Matter

    Pages 147-150

    PDF

These notes are the result of a course in dynamical systems given at Orsay during the 1976-77 academic year. I had given a similar course at the Gradu­ ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's n-Stability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M.

• dynamical systems
• manifold
• stability

• Thomas J. Watson Research Center, IBM, Yorktown Heights, USA

  Michael Shub

Policies and ethics