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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

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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