PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1994 | 145 | 1 | 65-77
Tytuł artykułu

Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps: geometric coding trees technique

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that if A is a basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then the periodic points in the boundary of A are dense in this boundary. To prove this in the non-simply connected or parabolic situations we prove a more abstract, geometric coding trees version.
Słowa kluczowe
Rocznik
Tom
145
Numer
1
Strony
65-77
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-04-30
poprawiono
1993-09-28
Twórcy
autor
  • Institute of Mathematics, Warsaw University, Banacha 2, 00-913 Warszawa, Poland, aniazd@mimuw.edu.pl
Bibliografia
  • [D] A. Douady, informal talk at the Durham Symposium, 1988.
  • [Du] P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York, 1970.
  • [EL] A. È. Eremenko and G. M. Levin, On periodic points of polynomials, Ukrain. Mat. Zh. 41 (1989), 1467-1471 (in Russian).
  • [F] P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France 48 (1920), 33-94.
  • [K] A. Katok, Lyapunov exponents, entropy and periodic points for diffeomorphisms, Publ. Math. IHES 51 (1980), 137-173.
  • [LP] G. Levin and F. Przytycki, External rays to periodic points, preprint 24 (1992/93), the Hebrew University of Jerusalem.
  • [Pe] C. L. Petersen, On the Pommerenke-Levin-Yoccoz inequality, Ergodic Theory Dynamical Systems 13 (1993), 785-806.
  • [Po] Ch. Pommerenke, On conformal mapping and iteration of rational functions, Complex Variables 5 (1986), 117-126.
  • [P1] F. Przytycki, Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map, Invent. Math. 80 (1985), 161-179.
  • [P2] F. Przytycki, Riemann map and holomorphic dynamics, ibid. 85 (1986), 439-455.
  • [P3] F. Przytycki, On invariant measures for iterations of holomorphic maps, in: Problems in Holomorphic Dynamics, preprint IMS 1992/7, SUNY at Stony Brook.
  • [P4] F. Przytycki, Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps, Fund. Math., to appear.
  • [PS] F. Przytycki and J. Skrzypczak, Convergence and pre-images of limit points for coding trees for iterations of holomorphic maps, Math. Ann. 290 (1991), 425-440.
  • [PUZ] F. Przytycki, M. Urbański and A. Zdunik, Harmonic, Gibbs and Hausdorff measures for holomorphic maps, Part 1: Ann. of Math. 130 (1989), 1-40; Part 2: Studia Math. 97 (1991), 189-225.
  • [Ro] V. A. Rokhlin, Lectures on the entropy theory of transformations with invariant measures, Uspekhi Mat. Nauk 22 (5) (1967), 3-56 (in Russian); English transl.: Russian Math. Surveys 22 (5) (1967), 1-52.
  • [R] D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Brasil. Math. 9 (1978), 83-87.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv145i1p65bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.