The size of quadratic p-adic linearization disks

作者：Lindahl Karl Olof^*

来源：Advances in Mathematics, 2013, 248: 872-894.

DOI：10.1016/j.aim.2013.07.020

• Small divisors
• Linearization
• p-adic numbers
• Ramification
• Periodic points

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

• 出版日期2013-11-25