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Wild recurrent critical points

Juan Rivera-Letelier
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Abstract

It is conjectured that a rational map whose coefficients are algebraic over $\Q_p$ has no wandering components of the Fatou set. R. Benedetto has shown that any counter example to this conjecture must have a wild recurrent critical point. We provide here the first examples of rational maps whose coefficients are algebraic over $\Q_p$ and that have a (wild) recurrent critical point. In fact, we show that there is such a rational map in every one parameter family of rational maps that is defined over a finite extension of $\Q_p$ and that has a Misiurewicz bifurcation.

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Juan Rivera-Letelier. 2004-06-21. Wild recurrent critical points. https://arxiv.org/abs/math/0406417

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