Attraction rates for iterates of a superattracting skew product

2021/05/10 by Kohei Ueno, Ueno, Kohei
Mathematics · #32H50(Primary) #37F80(Secondary) #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2105.04068

openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(z,w)=(p(z),q(z,w)) be a holomorphic skew product with a superattracting fixed point at the origin. In the previous paper we have succeeded to specify a dominant term of q by the order of p and the Newton polygon of q and to construct a Böttcher coordinate on an invariant wedge. By using the same idea and terminologies, we give inequalities of attraction rates for the vertical dynamics of f in this paper. The results hold not only for the superattracting case, but for all the other cases.

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