Topological classification of families of diffeomorphisms without small divisors /
[Book]
Javier Ribón
Providence, R.I. :
American Mathematical Society,
2010
1008
ix, 166 p. :
ill. ;
25 cm
Memoirs of the American Mathematical Society,
no. 975
0065-9266 ;
"Volume 207, number 975 (end of volume )."
Includes bibliographical references (p. 163) and index
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
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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."--Publisher's description