Summability implies Collet-Eckmann almost surely

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.

25 pages

References in corpus (2)

• On stochastic stability of non-uniformly expanding interval maps
• Nonuniformly expanding 1d maps with logarithmic singularities

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