Local indices of iterations of a holomorphic map
type: Item
instance of: scholarly article
title: Local indices of iterations of a holomorphic map
zbMATH Open document ID: 0673.32002
DOI: 10.1007/BF01078574
publication date: 1989-01-01T00:00:00Z
review text: Let \(f: (U,0)\to ({\mathbb R}^ m,0)\) be a \(C^ 1\) map of a neighborhood \(U\) of \(0\) such that \(0\) is an isolated fixed point for any iteration of \(f\). By results of Zabreĭko and Krasnosel'skii, Dold, and Shub and Sullivan, there is a (finite) sequence of integer numbers \(A_ d\) such that the indices of iterations of \(f\) at \(0\) can be written \(i(f^ n,0)=\sum_{d| n}dA_ d\), \(n=1,2,... \). In this paper the author shows that if \(f\) is complex analytic (then \(m=2k\) and \({\mathbb R}^ m={\mathbb C}^ k)\) then the multiplicities \(A_ d\) are submitted to some restrictions. A complete discussion is given by the author only in the \({\mathbb C}^ 2\) case.
Mathematics Subject Classification ID: 32A10
zbMATH DE Number: 4101570
zbMATH Keywords: iteration of analytic maps
zbMATH Keywords: local indices of iterations
author: S. A. Bogatyi
reviewed by: Wiesław Pleśniak
MaRDI profile type: Publication
cites work: Fixed point indices of iterated maps
cites work: Q5683986
cites work: A remark on the Lefschetz fixed point formula for differentiable maps
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4101570