On deterministic perturbations of non-uniformly expanding interval maps

Mathematics – Dynamical Systems

Scientific paper

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21 pages

Scientific paper

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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