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Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative

Artur Avila·Carlos Gustavo Moreira
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Abstract

We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-regular parameter is Collet-Eckmann with subexponential recurrence of the critical orbit. Those conditions lead to a detailed and robust statistical description of the dynamics. This proves the Palis conjecture in this setting.

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Artur Avila, Carlos Gustavo Moreira. 2003-06-10. Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative. https://arxiv.org/abs/math/0105221

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