Rivera-Letelier, Juan Wild recurrent critical points. (English) Zbl 1130.37378 J. Lond. Math. Soc., II. Ser. 72, No. 2, 305-326 (2005). Summary: It is conjectured that a rational map whose coefficients are algebraic over \(\mathbb{Q}_p\) 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 \(\mathbb{Q}_p\) 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 \(\mathbb{Q}_p\) and that has a Misiurewicz bifurcation. Cited in 4 Documents MSC: 37F50 Small divisors, rotation domains and linearization in holomorphic dynamics 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 11S85 Other nonanalytic theory × Cite Format Result Cite Review PDF Full Text: DOI arXiv