Compacts connexes invariants par une application univalente

• Autorzy: Emmanuel Risler
• Języki publikacji: FR

Abstrakty

EN

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.

Kategorie tematyczne

• 30D40: Cluster sets, prime ends, boundary behavior

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 161
• Numer: 3
• Strony: 241-277

Daty

wydano

1999

otrzymano

1998-04-14

poprawiono

1999-03-02

Twórcy

autor

Emmanuel Risler

• Institut Non Linéaire de Nice, UMR CNRS-UNSA 6618, 1361 route des Lucioles, F-06560 Valbonne, France

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