Repellers for real analytic maps

David Ruelle

Type: Article

Publication Date: 1982-03-01

Citations: 457

DOI: https://doi.org/10.1017/s0143385700009603

Abstract

Abstract The purpose of this note is to prove a conjecture of D. Sullivan that when the Julia set J of a rational function f is hyperbolic, the Hausdorff dimension of J depends real analytically on f . We shall obtain this as corollary of a general result on repellers of real analytic maps (see corollary 5).

Locations

Ergodic Theory and Dynamical Systems - View - PDF

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