Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
type: Item
instance of: scholarly article
title: Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
zbMATH Open document ID: 1372.37046
author: Grzegorz Graff
author: Jerzy Jezierski
published in: Geometriae Dedicata
publication date: 2017-04-13T00:00:00Z
review text: Consider the family of self maps \(f: M\to M\) of a compact simply-connected manifold of dimension greater or equal to 4, whose boundary is simply-connected as well. Given an odd natural number \(r\), this paper describes an invariant that associates to \(f\) the minimal number of \(r\)-periodic orbits for all maps over the \(C^1\)-homotopy class of \(f\) that preserve the boundary of \(M\). Necessary and sufficient conditions for the reduction of a set of \(r\)-periodic points to one in the \(C^1\)-homotopy class are given as application.
reviewed by: Marco Spadini
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 37C05
zbMATH DE Number: 6705655
zbMATH Keywords: periodic point
zbMATH Keywords: boundary-preserving map
zbMATH Keywords: Nielsen number
zbMATH Keywords: fixed point index
zbMATH Keywords: smooth map
Wikidata QID: Q59609046
MaRDI profile type: Publication
full work available at URL: s10711-016-0199-4
OpenAlex ID: W2531602033
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DOI: 10.1007/S10711-016-0199-4
description: scientific article; zbMATH DE number 6705655