J-Stability in non-archimedean dynamics

Abstract

Let $C_v$ be a complete, algebraically closed non-archimedean field, and let $f\in C_v(z)$ be a rational function of degree $d\ge 2$. 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.

26 pages. Extended Theorem 1.1 to show continuous motion of Julia sets. Accepted in Advances in Mathematics