The size of quadratic p-adic linearization disks

We find the exact radius of linearization disks at indifferent fixed points of quadratic maps in Cp. 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 Cp where the boundary of the linearization disk does not contain any periodic point.