9. Smale’s horseshoe and chaos

Chapters in this book

1. Frontmatter I
2. Contents V
3. Preface to the first edition IX
4. Preface to the second edition XIII
5. List of main symbols XV
6. 1. Dynamical systems 1
7. 2. Topologies on spaces of dynamical systems 16
8. 3. Equivalence relations 26
9. 4. Hyperbolic fixed point 37
10. 5. Hyperbolic rest point and hyperbolic closed trajectory 66
11. 6. Transversality 77
12. 7. Hyperbolic sets 90
13. 8. Anosov diffeomorphisms 116
14. 9. Smale’s horseshoe and chaos 123
15. 10. Closing lemma 131
16. 11. C⁰-generic properties of dynamical systems 136
17. 12. Shadowing of pseudotrajectories in dynamical systems 153
18. 13. Invariant measures 174
19. A. Scheme of the proof of the Mañé theorem 196
20. B. Lectures on selected chapters of the history of differential equations and dynamical systems 206
21. Bibliography 236
22. Index 239