Expanding repellers in limit sets for iterations of holomorphic functions

• Autorzy: Feliks Przytycki
• Języki publikacji: EN

Abstrakty

EN

We prove that for Ω being an immediate basin of attraction to an attracting fixed point for a rational mapping of the Riemann sphere, and for an ergodic invariant measure μ on the boundary FrΩ, with positive Lyapunov exponent, there is an invariant subset of FrΩ which is an expanding repeller of Hausdorff dimension arbitrarily close to the Hausdorff dimension of μ. We also prove generalizations and a geometric coding tree abstract version. The paper is a continuation of a paper in Fund. Math. 145 (1994) by the author and Anna Zdunik, where the density of periodic orbits in FrΩ was proved.

Kategorie tematyczne

• 37F35: Conformal densities and Hausdorff dimension
• 37F15: Expanding maps; hyperbolicity; structural stability
• 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 186
• Numer: 1
• Strony: 85-96

Daty

wydano

2005

Twórcy

autor

Feliks Przytycki

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm186-1-7