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Collet–Eckmann condition for recurrent critical orbits implies uniform hyperbolicity on periodic orbits

Published online by Cambridge University Press:  03 May 2007

NICOLAE MIHALACHE
NICOLAE MIHALACHE
Affiliation:
Department of Mathematics, University Paris XI, Orsay 91405, France (e-mail: nicolae.mihalache-ciurdea@math.u-psud.fr)
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Abstract

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We prove that the Collet–Eckmann condition for recurrent critical orbits inside the Julia set of a rational map with no parabolic periodic orbits implies uniform hyperbolicity on periodic orbits.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007, pp. 1267 - 1286
Copyright
2007 Cambridge University Press