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Summability implies Collet–Eckmann almost surely

Published online by Cambridge University Press:  21 January 2013

BING GAO  and
WEIXIAO SHEN
BING GAO
Affiliation:
Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singaporeg0901232@nus.edu.sgmatsw@nus.edu.sg
WEIXIAO SHEN
Affiliation:
Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singaporeg0901232@nus.edu.sgmatsw@nus.edu.sg
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Abstract

We provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family ${f}_{t} $ of maps with ${f}_{0} = f$, we prove that $t= 0$ is a Lebesgue density point of the set of parameters for which ${f}_{t} $ satisfies both the Collet–Eckmann condition and a strong polynomial recurrence condition.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1184 - 1209
Copyright
Copyright © Cambridge University Press 

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