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Topological Classification of Families of Diffeomorphisms without Small Divisors
Javier Ribón, University Federal Fluminense, Centro, Niterói, Brazil
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Memoirs of the American Mathematical Society
2010; 166 pp; softcover
Volume: 207
ISBN-10: 0-8218-4748-1
ISBN-13: 978-0-8218-4748-0
List Price: US$77
Individual Members: US$46.20
Institutional Members: US$61.60
Order Code: MEMO/207/975
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The author gives a complete topological classification for germs of one-parameter families of one-dimensional complex analytic diffeomorphisms without small divisors. In the non-trivial cases the topological invariants are given by some functions attached to the fixed points set plus the analytic class of the element of the family corresponding to the special parameter. The proof is based on the structure of the limits of orbits when we approach the special parameter.

Table of Contents

  • Outline of the monograph
  • Flower type vector fields
  • A clockwork orange
  • The T-sets
  • The long limits
  • Topological conjugation of (NSD) vector fields
  • Families of diffeomorphisms without small divisors
  • Topological invariants of (NSD) diffeomorphisms
  • Tangential conjugations
  • List of notations
  • Bibliography
  • Index
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