Advertisement

Mathematische Annalen

, Volume 290, Issue 1, pp 425–440 | Cite as

Convergence and pre-images of limit points for coding trees for iterations of holomorphic maps

  • Feliks Przytycki
  • Jan Skrzypczak
Article

Keywords

Limit Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B]
    Beurling, A.: Ensembles exceptionelles. Acta Math.72, 1–12 (1940)Google Scholar
  2. [C]
    Carleson, L.: Selected problems on exceptional sets. Princeton Melbourne: Van Nostrand 1967Google Scholar
  3. [H]
    Hille, E.: Analytic functions theory. Boston: Ginn 1962Google Scholar
  4. [Ja]
    Jakobson, M.V.: Markov partitions for rational endomorphisms of the Riemann sphere. Mnogokomponientnyje slučajnyje sistemy, pp. 303–319, Moscow: Nauka 1978 (in Russian)Google Scholar
  5. [LP]
    Langevin, R., Przytycki, F.: Entropie de l'image inverse d'applications (to appear)Google Scholar
  6. [M]
    Misiurewicz, M.: On expanding maps of compact manifolds and local homeomorphisms of a circle. Bull. Acad. Pol. Sci. Ser. Math. Astr. Phys.18, 725–732 (1970)Google Scholar
  7. [Lyu1]
    Lyubich, M.: Entropy of analytic endomorphisms of the Riemann sphere. Funkts. Anal. Prilozh.15.4, 83–84 (1981)Google Scholar
  8. [Lyu2]
    Lyubich, M.: Entropy properties of rational endomorphisms of the Riemann sphere. Ergodic Theory Dyn. Syst.3, 351–386 (1983)Google Scholar
  9. [P1]
    Przytycki, F.: Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map. Invent. Math.80, 161–179 (1985)Google Scholar
  10. [P2]
    Przytycki, F.: Riemann map and holomorphic dynamics. Invent. Math.85, 439–455 (1986)Google Scholar
  11. [P3]
    Przytycki, F.: On the Perron-Frobenius-Ruelle operator for rational maps on the Riemann sphere and for Hölder continuous function. Biol. Soc. Bras. Mat.20.2, 95–125 (1990)Google Scholar
  12. [P4]
    Przytycki, F.: Convergence of coding trees for holomorphic dynamics. Preprint, Inst. Maty. PAN (1988)Google Scholar
  13. [PUZ]
    Przytycki, F., Urbański, M., Zdunik, A.: Harmonic, Gibbs and Hausdorff measures on reperellers for holomorphic maps. Part I in Ann. Math.130, 1–40 (1989), Part II to appear in Stud. Math. 97.3Google Scholar
  14. [S]
    Skrzypczak, J.: Preimages of limit points for coding trees. Preprint, Inst. Math. PAN (1989)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Feliks Przytycki
    • 1
  • Jan Skrzypczak
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesWarszawaPoland
  2. 2.Institute of MathematicsWarsaw UniversityWarszawaPoland

Personalised recommendations