AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
Unfoldings and bifurcations of quasi-periodic tori
About this Title
H. W. Broer, G. B. Huitema, F. Takens and B. L. J. Braaksma
Publication: Memoirs of the American Mathematical Society
Publication Year:
1990; Volume 83, Number 421
ISBNs: 978-0-8218-2483-2 (print); 978-1-4704-0844-2 (online)
DOI: https://doi.org/10.1090/memo/0421
MathSciNet review: 1041003
MSC: Primary 58F27; Secondary 34C35, 34D30, 58C27, 58F14, 58F30, 70H05
Table of Contents
Chapters
- Part I. Unfoldings of quasi-periodic tori (by H. W. Broer, G. B. Huitema and F. Takens)
- 1. Introduction
- 2. Preliminaries
- 3. The integrable case
- 4. The nearly integrable case in the general (dissipative) context
- 5. The nearly integrable cases in the volume preserving and the symplectic ($m$ = $n$) contexts
- 6. The nearly integrable case in the general symplectic context
- 7. Applications—Related results
- 8. Proof of the main result
- Part II. Toward a quasi-periodic bifurcation theory (by B. L. J. Braaksma, H. W. Broer and G. B. Huitema)
- 1. Introduction
- 2. A higher order normal form theory
- 3. The bifurcation models
- 4. Applications
- 5. Proof of the Saddle–Node Stability Theorem
- Appendix