Partially periodic point free self-maps on product of spheres and Lie groups
type: Item
instance of: scholarly article
title: Partially periodic point free self-maps on product of spheres and Lie groups
zbMATH Open document ID: 1458.37012
published in: Qualitative Theory of Dynamical Systems
publication date: 2020-10-12T00:00:00Z
review text: Let \(X\) be a topological manifold and \(f:X\to X\) a continuous map. The map \(f\) is said to be partially periodic point free up to period \(n\) if \(f\) does not have periodic points of periods smaller than \(n+1\). Similarly \(f\) is Lefschetz periodic point free if the Lefschetz numbers of all iterates of \(f\) are zero. In this paper the author considers continuous self-maps on products of any number spheres of different dimensions and present necessary and sufficient conditions for such maps to be Lefschetz periodic point free and Lefschetz partially periodic point free. The results are applied to continuous self-maps on Lie groups.
reviewed by: Weslem L. Silva
Mathematics Subject Classification ID: 37B02
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37E15
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 7259351
zbMATH Keywords: Lefschetz numbers
zbMATH Keywords: periodic point
zbMATH Keywords: product of spheres
zbMATH Keywords: Lie groups
author: Víctor F. Sirvent
MaRDI profile type: Publication
full work available at URL: s12346-020-00419-9
OpenAlex ID: W3083708806
Wikidata QID: Q115376675
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DOI: 10.1007/S12346-020-00419-9
description: scientific article; zbMATH DE number 7259351