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arXiv · 1811.07198

Rational maps with bad reduction and domains of quasiperiodicity

Víctor Nopal-Coello·Mónica Moreno Rocha
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Abstract

Consider a rational map $R$ of degree $d\geq 2$ with coefficients over the non-archimedean field $\mathbb{C}_p$, 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.

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Víctor Nopal-Coello, Mónica Moreno Rocha. 2018-11-17. Rational maps with bad reduction and domains of quasiperiodicity. https://arxiv.org/abs/1811.07198

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