PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1996 | 150 | 3 | 237-244
Tytuł artykułu

Rigidity of harmonic measure

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical system to another one for which the harmonic measure equals the measure of maximal entropy.
Słowa kluczowe
Rocznik
Tom
150
Numer
3
Strony
237-244
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-04-28
poprawiono
1995-12-29
Twórcy
autor
  • Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A., irina@math.msu.edu
  • Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A., volberg@math.msu.edu
Bibliografia
  • [B] Z. Balogh, Rigidity of harmonic measure on totally disconnected fractals, preprint, Michigan State University, April 1995.
  • [BPV] Z. Balogh, I. Popovici and A. Volberg, Conformally maximal polynomial-like dynamics and invariant harmonic measure, preprint, Uppsala Univ., U.U.D.M. Report 1994:32.
  • [BV] Z. Balogh et A. Volberg, Principe de Harnack à la frontière pour des répulseurs holomorphes non récurrents, C. R. Acad. Sci. Paris 319 (1994), 351-354.
  • [Br] H. Brolin, Invariant sets under iteration of rational functions, Ark. Mat. 6 (1965), 103-145.
  • [DH] A. Douady and F. Hubbard, On the dynamics of polynomial like mappings, Ann. Sci. Ecole Norm. Sup. 18 (1985), 287-345.
  • [Fo] S. R. Foguel, The Ergodic Theory of Markov Processes, Math. Stud. 21, Van Nostrand, New York, 1969.
  • [FLM] A. Freire, A. Lopes and R. Ma né, An invariant measure for rational maps, Bol. Soc. Brasil Mat. 14 (1983), 45-62.
  • [Lo] A. Lopes, Equilibrium measure for rational functions, Ergodic Theory Dynam. Systems 6 (1986), 393-399.
  • [Ly1] M. Lyubich, Entropy of the analytic endomorphisms of the Riemann sphere, Funktsional. Anal. i Prilozhen. 15 (4) (1981), 83-84 (in Russian).
  • [Ly2] M. Lyubich, Entropy properties of rational endomorphisms of the Riemann sphere, Ergodic Theory Dynam. Systems 3 (1983), 351-386.
  • [LV] M. Yu. Lyubich and A. Volberg, A comparison of harmonic and maximal measures on Cantor repellers, J. Fourier Anal. Appl. 1 (1995), 359-379.
  • [M] R. Ma né, On the uniqueness of the maximizing measure for rational maps, Bol. Soc. Brasil. Mat. 14 (1983), 27-43.
  • [MR] R. Ma né and L. F. da Rocha, Julia sets are uniformly perfect, Proc. Amer. Math. Soc. 116 (1992), 251-257.
  • [SS] M. Shub and D. Sullivan, Expanding endomorphisms of the circle revisited, Ergodic Theory Dynam. Systems 5 (1985), 285-289.
  • [Z1] A. Zdunik, Parabolic orbifolds and the dimension of the maximal measure for rational maps, Invent. Mat. 99 (1990), 627-649.
  • [Z2] A. Zdunik, Invariant measure in the class of harmonic measures for polynomial-like mappings, preprint 538, Inst. Math., Polish Acad. Sci., 1995.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv150i3p237bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.