Realization of all Dold's congruences with stability
type: Item
instance of: scholarly article
title: Realization of all Dold's congruences with stability
zbMATH Open document ID: 1208.37014
published in: Journal of Differential Equations
publication date: 2010-07-22T00:00:00Z
full work available at URL: 2010realization.pdf
review text: This paper is concerned with sequences of integers satisfying Dold's congruences. In particular, it deals with the sequences of fixed point indices, at an isolated stable fixed point, of the iterations of a orientation-preserving homeomorphisms. The main result states that for each \(n>2\) and for every sequence \(\{I_m\}_{m\in{\mathbb N}}\) satisfying Dold's congruences there exists an orientation preserving homeomorphism \(h:{\mathbb R}^n\to{\mathbb R}^n\) such that the fixed point and the periodic point sets of \(h\) coincide with the origin \(\bar 0\) of \({\mathbb R}^n\), which is a stable equilibrium of \(h\), and the fixed point index \(i(h^m,\bar 0)\) at \(\bar 0\) is given by \(I_m\) for any \(m\in{\mathbb N}\). This fact can be used to deduce that in a dimension \(n> 2\) not all sequences are realized (in the above sense) by homeomorphisms and can also be realized by diffeomorphisms.
reviewed by: Marco Spadini
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37B30
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5759048
zbMATH Keywords: Conley index
zbMATH Keywords: fixed point index
zbMATH Keywords: stable fixed points
zbMATH Keywords: homeomorphisms
author: Francisco R. Ruiz del Portal
author: José Miguel Salazar
MaRDI profile type: Publication
OpenAlex ID: W2169433502
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DOI: 10.1016/J.JDE.2010.03.006
description: scientific article; zbMATH DE number 5759048