Wild recurrent critical points

• Autores: Juan Rivera-Letelier
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 72, Nº 2, 2005, págs. 305-326
• Idioma: inglés
• DOI: 10.1112/s0024610705006885
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• Resumen

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