2018/11/17 by Víctor Nopal-Coello, Nopal-Coello, Víctor, Mónica Moreno Rocha +1
Mathematics · #11S82(Primary) 37P05 #37P40 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1811.07198
openalex publication_date 2018/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Consider a rational map R of degree d≥ 2 with coefficients over the non-archimedean field ℂp, with p a fixed prime number. If R has a cycle of Siegel disks and has good reduction, then it was shown by Rivera-Letelier in his PhD dissertation that a new rational map Q can be constructed from R, in such a way that Q will exhibit a cycle of m-Herman rings. In this paper, we address the case of rational maps with bad reduction and provide an extension of Rivera-Letelier's result for these class of maps.