Compacts connexes invariants par une application univalente

Emmanuel Risler

Fundamenta Mathematicae (1999)

  • Volume: 161, Issue: 3, page 241-277
  • ISSN: 0016-2736


Let K be a compact connected subset of cc, not reduced to a point, and F a univalent map in a neighborhood of K such that F(K) = K. This work presents a study and a classification of the dynamics of F in a neighborhood of K. When ℂ K has one or two connected components, it is proved that there is a natural rotation number associated with the dynamics. If this rotation number is irrational, the situation is close to that of “degenerate Siegel disks” or “degenerate Herman rings” studied by R. Pérez-Marco (in particular, any point of K is recurrent). In any other case (that is, if this number is rational or if ℂ K has more than two connected components), the situation is essentially trivial: the dynamics is of Morse-Smale type, and a complete description and classification modulo analytic conjugacy is given.

How to cite


Risler, Emmanuel. "Compacts connexes invariants par une application univalente." Fundamenta Mathematicae 161.3 (1999): 241-277. <>.

author = {Risler, Emmanuel},
journal = {Fundamenta Mathematicae},
keywords = {complex dynamic; univalent map; rotation number},
language = {fre},
number = {3},
pages = {241-277},
title = {Compacts connexes invariants par une application univalente},
url = {},
volume = {161},
year = {1999},

AU - Risler, Emmanuel
TI - Compacts connexes invariants par une application univalente
JO - Fundamenta Mathematicae
PY - 1999
VL - 161
IS - 3
SP - 241
EP - 277
LA - fre
KW - complex dynamic; univalent map; rotation number
UR -
ER -


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