There are no proper topological hyperbolic homoclinic classes for area-preserving maps

doi:10.1017/S0013091519000282

Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/64189

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DC Field	Value	Language
dc.contributor.author	Bessa, Mário	por
dc.contributor.author	Torres, M. J.	por
dc.date.accessioned	2020-03-03T13:35:50Z	-
dc.date.available	2020-03-03T13:35:50Z	-
dc.date.issued	2020	-
dc.identifier.issn	0013-0915	por
dc.identifier.uri	https://hdl.handle.net/1822/64189	-
dc.description.abstract	We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class \Lambda associated to an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then \Lambda=M and f is an Anosov homeomorphism.	por
dc.description.sponsorship	MB was partially supported by FCT - ‘Fundação para a Ciência e a Tecnologia’, through Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, project UID/MAT/00212/2013. MJT was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the ‘Fundação para a Ciência e a Tecnologia’, through the Project UID/MAT/00013/2013.	por
dc.language.iso	eng	por
dc.publisher	Cambridge University Press	por
dc.relation	info:eu-repo/grantAgreement/FCT/5876/147408/PT	por
dc.relation	info:eu-repo/grantAgreement/FCT/5876/147370/PT	por
dc.rights	openAccess	por
dc.subject	Shadowing	por
dc.subject	Expansiveness	por
dc.subject	Topological dynamics	por
dc.subject	Homoclinic classes	por
dc.title	There are no proper topological hyperbolic homoclinic classes for area-preserving maps	por
dc.type	article	por
dc.peerreviewed	yes	por
dc.relation.publisherversion	https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/there-are-no-proper-topological-hyperbolic-homoclinic-classes-for-areapreserving-maps/4232BAC3B800704E53605E9CAF044072	por
oaire.citationStartPage	217	por
oaire.citationEndPage	228	por
oaire.citationIssue	1	por
oaire.citationVolume	63	por
dc.identifier.eissn	1464-3839	por
dc.identifier.doi	10.1017/S0013091519000282	por
dc.subject.fos	Ciências Naturais::Matemáticas	por
dc.subject.wos	Science & Technology	por
sdum.journal	Proceedings of the Edinburgh Mathematical Society	por
oaire.version	AM	por
Appears in Collections:	CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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