Wild recurrent critical points

2004/06/21 by Juan Rivera-Letelier, Juan Rivera‐Letelier, Rivera-Letelier, Juan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.math/0406417

arxiv created 2004/06/21 · openalex publication_date 2004/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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