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Hausdorff dimension of Julia sets of complex Hénon mappings

Published online by Cambridge University Press:  19 September 2008

A. Verjovsky  and
H. Wu
A. Verjovsky
Affiliation:
UFR de Mathématiques, Université des Sciences et Technologies de Lille 1, 59655 Villeneuve D'Ascq, Lille, France
H. Wu
Affiliation:
Einstein Chair, City University of New York, 33 West 42 Street, New York, NY 10036-8099, USA
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Abstract

The Hausdorff dimension of closed invariant sets under diffeomorphisms is an interesting concept as it is a measure of their complexity. The theory of holomorphic dynamical systems provides us with many examples of fractal sets and, in particular, a theorem of Ruelle [Ru1] shows that the Hausdorff dimension of the Julia set depends real analytically on f if f is a rational function of ℂ and the Julia set J of f is hyperbolic. In this paper we generalize Ruelle's result for complex dimension two and show the real analytic dependence of the Hausdorff dimension of the corresponding Julia sets of hyperbolic Hénon mappings.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 849 - 861
Copyright
Copyright © Cambridge University Press 1996

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