Epsilon Nielsen fixed point theory

<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-29470-i1.gif"/></inline-formula> be a map of a compact, connected Riemannian manifold, with or without boundary. For <inline-formula><graphic file="1687-1812-2006-29470-i2.gif"/>&l...

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Autor principal:	Brown Robert F
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2006
Materias:	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/26cdabb7468f445fb36fa5f37e435c03
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spelling	oai:doaj.org-article:26cdabb7468f445fb36fa5f37e435c032021-12-02T10:59:31ZEpsilon Nielsen fixed point theory1687-18201687-1812https://doaj.org/article/26cdabb7468f445fb36fa5f37e435c032006-01-01T00:00:00Zhttp://www.fixedpointtheoryandapplications.com/content/2006/29470https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-29470-i1.gif"/></inline-formula> be a map of a compact, connected Riemannian manifold, with or without boundary. For <inline-formula><graphic file="1687-1812-2006-29470-i2.gif"/></inline-formula> sufficiently small, we introduce an <inline-formula><graphic file="1687-1812-2006-29470-i3.gif"/></inline-formula>-Nielsen number <inline-formula><graphic file="1687-1812-2006-29470-i4.gif"/></inline-formula> that is a lower bound for the number of fixed points of all self-maps of <inline-formula><graphic file="1687-1812-2006-29470-i5.gif"/></inline-formula> that are <inline-formula><graphic file="1687-1812-2006-29470-i6.gif"/></inline-formula>-homotopic to <inline-formula><graphic file="1687-1812-2006-29470-i7.gif"/></inline-formula>. We prove that there is always a map <inline-formula><graphic file="1687-1812-2006-29470-i8.gif"/></inline-formula> that is <inline-formula><graphic file="1687-1812-2006-29470-i9.gif"/></inline-formula>-homotopic to <inline-formula><graphic file="1687-1812-2006-29470-i10.gif"/></inline-formula> such that <inline-formula><graphic file="1687-1812-2006-29470-i11.gif"/></inline-formula> has exactly <inline-formula><graphic file="1687-1812-2006-29470-i12.gif"/></inline-formula> fixed points. We describe procedures for calculating <inline-formula><graphic file="1687-1812-2006-29470-i13.gif"/></inline-formula> for maps of <inline-formula><graphic file="1687-1812-2006-29470-i14.gif"/></inline-formula>-manifolds.</p> Brown Robert FSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2006, Iss 1, p 29470 (2006)
institution	DOAJ
collection	DOAJ
language	EN
topic	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Brown Robert F Epsilon Nielsen fixed point theory
description	<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-29470-i1.gif"/></inline-formula> be a map of a compact, connected Riemannian manifold, with or without boundary. For <inline-formula><graphic file="1687-1812-2006-29470-i2.gif"/></inline-formula> sufficiently small, we introduce an <inline-formula><graphic file="1687-1812-2006-29470-i3.gif"/></inline-formula>-Nielsen number <inline-formula><graphic file="1687-1812-2006-29470-i4.gif"/></inline-formula> that is a lower bound for the number of fixed points of all self-maps of <inline-formula><graphic file="1687-1812-2006-29470-i5.gif"/></inline-formula> that are <inline-formula><graphic file="1687-1812-2006-29470-i6.gif"/></inline-formula>-homotopic to <inline-formula><graphic file="1687-1812-2006-29470-i7.gif"/></inline-formula>. We prove that there is always a map <inline-formula><graphic file="1687-1812-2006-29470-i8.gif"/></inline-formula> that is <inline-formula><graphic file="1687-1812-2006-29470-i9.gif"/></inline-formula>-homotopic to <inline-formula><graphic file="1687-1812-2006-29470-i10.gif"/></inline-formula> such that <inline-formula><graphic file="1687-1812-2006-29470-i11.gif"/></inline-formula> has exactly <inline-formula><graphic file="1687-1812-2006-29470-i12.gif"/></inline-formula> fixed points. We describe procedures for calculating <inline-formula><graphic file="1687-1812-2006-29470-i13.gif"/></inline-formula> for maps of <inline-formula><graphic file="1687-1812-2006-29470-i14.gif"/></inline-formula>-manifolds.</p>
format	article
author	Brown Robert F
author_facet	Brown Robert F
author_sort	Brown Robert F
title	Epsilon Nielsen fixed point theory
title_short	Epsilon Nielsen fixed point theory
title_full	Epsilon Nielsen fixed point theory
title_fullStr	Epsilon Nielsen fixed point theory
title_full_unstemmed	Epsilon Nielsen fixed point theory
title_sort	epsilon nielsen fixed point theory
publisher	SpringerOpen
publishDate	2006
url	https://doaj.org/article/26cdabb7468f445fb36fa5f37e435c03
work_keys_str_mv	AT brownrobertf epsilonnielsenfixedpointtheory
_version_	1718396342809657344

Epsilon Nielsen fixed point theory

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