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arXiv · 2103.17200

Critical recurrence in the real quadratic family

Mats Bylund
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Abstract

We study recurrence in the real quadratic family and give a sufficient condition on the recurrence rate $(\delta_n)$ of the critical orbit such that, for almost every nonregular parameter $a$, the set of $n$ such that $\vert F^n(0;a) \vert < \delta_n$ is infinite. In particular, when $\delta_n = n^{-1}$, this extends an earlier result of Avila and Moreira.

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Mats Bylund. 2021-03-31. Critical recurrence in the real quadratic family. https://doi.org/10.1017/etds.2022.78

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