A construction of Böttcher coordinates for holomorphic skew products. (18th June 2019)

• Record Type: Journal Article
• Authors: Ueno, Kohei
• Is Part Of: Nonlinearity. Volume 32:Number 7(2019)
• Page Start: 2694
• Page End: 2720
• Publication Date: 2019-06-18
• Subjects: complex dynamics -- Böttcher coordinates -- superattracting fixed points -- skew products -- Newton polygons blow-ups -- branched coverings; Primary 32H50 -- Secondary 37F50; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab0914
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Let be a holomorphic skew product with a superattracting fixed point at the origin. Under one or two assumptions, we prove that f is conjugate to a monomial map on an invariant open set whose closure contains the origin. The monomial map and the open set are determined by the degree of p and the Newton polygon of q .