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Mathematics  2011 

Summability implies Collet-Eckmann almost surely

DOI: 10.1017/etds.2012.173

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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 Collect-Eckmann condition and a strong polynomial recurrence condition.

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