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Generic bifurcations for involutory area preserving maps

About this Title

Russell J. Rimmer

Publication: Memoirs of the American Mathematical Society
Publication Year: 1983; Volume 41, Number 272
ISBNs: 978-0-8218-2272-2 (print); 978-1-4704-0682-0 (online)
DOI: https://doi.org/10.1090/memo/0272
MathSciNet review: 683419
MSC: Primary 58F14; Secondary 34C25, 58F05

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Preliminaries
  • 3. Bifurcation from a symmetric fixed point with multipliers $\pm 1$
  • 4. Conditions on generating functions occur generically
  • 5. Bifurcation from a symmetric fixed point $u_0$ of $\phi _{e_0}$ with multipliers which are $n^{\textrm {th}}$ prime roots of unity, for $n\geq 3$
  • 6. Normalisation of a family of involutory area preserving maps
  • 7. Generic bifurcations
  • 8. Families of involutory area preserving maps and symmetric Hamiltonian systems
  • Appendix