PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 161 | 3 | 241-277
Tytuł artykułu

Compacts connexes invariants par une application univalente

Autorzy
Treść / Zawartość
Warianty tytułu
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.
Słowa kluczowe
Rocznik
Tom
161
Numer
3
Strony
241-277
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-04-14
poprawiono
1999-03-02
Twórcy
  • Institut Non Linéaire de Nice, UMR CNRS-UNSA 6618, 1361 route des Lucioles, F-06560 Valbonne, France
Bibliografia
  • [B] G. D. Birkhoff, Sur quelques courbes fermées remarquables, Bull. Soc. Math. France 60 (1932), 1-26.
  • [C,G] L. Carleson and T. W. Gamelin, Complex Dynamics, Springer, 1993.
  • [C,L] M. L. Cartwright and J. C. Littlewood, Some fixed point theorems, Ann. of Math. 54 (1951), 1-37.
  • [E] J. Ecalle, Théorie des invariants holomorphes, Publ. Math. Orsay 67, 7409 (1974).
  • [H1] M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. I.H.E.S. 49 (1979), 5-233.
  • [H2] M. R. Herman, Are there critical points on the boundaries of singular domains?, Comm. Math. Phys. 99 (1985), 593-612.
  • [L] P. Le Calvez, Propriétés des attracteurs de Birkhoff, Ergodic Theory Dynam. Systems 8 (1987), 241-310.
  • [M] J. Mather, Commutators of diffeomorphisms, Comm. Math. Helv. 48 (1973), 195-233.
  • [P,Y] J. Palis and J.-C. Yoccoz, Differentiable conjugacies of Morse-Smale diffeomorphisms, Bol. Soc. Brasil. Mat. 20 (1990), 25-48.
  • [PM1] R. Pérez-Marco, Fixed points and circle maps, Acta Math. 179 (1997), 243-294.
  • [PM2] R. Pérez-Marco, Topology of Julia sets and hedgehogs, preprint, Université de Paris-Sud, 94-48, 1994.
  • [PM3] R. Pérez-Marco, Hedgehog's dynamics, preprint.
  • [PM4] R. Pérez-Marco, Classification dynamique des continua pleins invariants par un difféomorphisme holomorphe, manuscrit, 1996.
  • [Po] C. Pommerenke, Boundary Behaviour of Conformal Maps, Springer, 1992.
  • [V] S. M. Voronin, Analytic classification of germs of conformal mappings (ℂ,0) → (ℂ,0) with identity linear part, Funktsional. Anal. i Prilozhen. 15 (1981), no. 1, 1-17 (in Russian).
  • [Y] J.-C. Yoccoz, Conjugaison des difféomorphismes analytiques du cercle, manuscrit, 1988.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv161i3p241bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.