Growth of attraction rates for iterates of a superattracting germ in dimension two

2012/09/15 by W. J. Gignac, William Gignac, Gignac, William +2 · 1 citation
Mathematics · #13a18 #32h50 #37p50 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Meromorphic and Entire Functions #math.DS #msc:13a18 #msc:32h50 #msc:37p50

paper · pdf · doi:10.48550/arxiv.1209.3450

27 pages, 1 figure

openalex publication_date 2012/09/15 · arxiv created 2013/02/07 · arxiv updated 2013/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the sequence of attraction rates of iterates of a dominant superattracting holomorphic fixed point germ f:(C²,0)->(C²,0). By using valuative techniques similar to those developed by Favre-Jonsson, we show that this sequence eventually satisfies an integral linear recursion relation, which, up to replacing f by an iterate, can be taken to have order at most two. In addition, when the germ f is finite, we show the existence of a bimeromorphic model of (C²,0) where f satisfies a weak local algebraic stability condition.

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