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Repellers for real analytic maps

Published online by Cambridge University Press:  13 August 2009

David Ruelle
David Ruelle
Affiliation:
Institut des Hautes Etudes Scientifiques, 35, Route de Chartres, 91440 Bures-sur-Yvette, France
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Abstract

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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).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 1 , March 1982 , pp. 99 - 107
Copyright
Copyright © Cambridge University Press 1982

References

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