Title: Dynamics of superattracting skew products on the attracting basins: Böttcher coordinates and plurisubharmonic functions

Authors: Kohei Ueno

Addresses: Daido University, Nagoya 457-8530, Japan

Abstract: We study the dynamics of a superattracting skew product f on the attracting basin. As the first strategy, we find out forward f-invariant wedge-shaped regions in the basin, on some of which f is conjugate to monomial maps, and consider whether the unions of all the preimages of the regions coincide with the basin. As the second strategy, we show the existence and properties of several kinds of plurisubharmonic functions of f, the main functions of which are induced from the Böttcher coordinates, and investigate the asymptotic behaviour of the functions toward the boundaries of the unions. Consequently, we obtain a plurisubharmonic function on the complement of specific fibres in the basin, which is continuous and pluriharmonic on open and dense subsets of the complement and describes an certain weighted vertical dynamics well.

Keywords: complex dynamics; skew products; superattracting fixed points; Böttcher coordinates; plurisubharmonic functions.

DOI: 10.1504/IJDSDE.2025.146961

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.1/2, pp.143 - 198

Received: 20 Dec 2023
Accepted: 12 Mar 2025
Published online: 27 Jun 2025 *

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