arXiv:2102.05841 Abstract | arXiv Analytics

arXiv:2102.05841 [math.DS]Abstract References Reviews Resources

J-Stability in non-archimedean dynamics

Published 2021-02-11Version 1

Let $C_v$ be a complete, algebraically closed non-archimedean field, and let $f \in C_v(z)$ be a rational function of degree $d \geq 2$. If $f$ satisfies a bounded contraction condition on its Julia set, we prove that small perturbations of $f$ have dynamics conjugate to those of $f$ on their Julia sets.

Comments: 24 pages

Categories: math.DS, math.NT

Subjects: 37P40, 37P45, 37P50, 11S82, 37P05

Keywords: non-archimedean dynamics, julia set, j-stability, rational function, bounded contraction condition

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