The size of quadratic $p$-adic linearization disks

Abstract

We find the exact radius of linearization disks at indifferent fixed points of quadratic maps in ${\mathbb{C}}_p$. We also show that the radius is invariant under power series perturbations. Localizing all periodic orbits of these quadratic-like maps we then show that periodic points are not the only obstruction for linearization. In so doing, we provide the first known examples in the dynamics of polynomials over ${\mathbb{C}}_p$ where the boundary of the linearization disk does not contain any periodic point.

Published version available at http://www.sciencedirect.com/science/article/pii/S0001870813003083; 26 pages; 3 figures

References in corpus (2)

• Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture
• Polynomial Siegel disks are typically Jordan domains

Cited by in corpus (3)

• Characterization of 2-ramified power series
• Optimal cycles in ultrametric dynamics and minimally ramified power series
• Geometric location of periodic points of 2-ramified power series