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The connection between computability of a nonlinear problem and its linearization: the Hartman-Grobman theorem revisited

2012-10Journal article Open access
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dc.contributor.authorGraça, Daniel
dc.contributor.authorZhong, Ning
dc.contributor.authorDumas, H. S.
dc.date.accessioned2018-12-07T14:58:08Z
dc.date.available2018-12-07T14:58:08Z
dc.date.issued2012-10
dc.description.abstractAs one of the seven open problems in the addendum to their 1989 book Computability in Analysis and Physics Pour-El and Richards (1989)[17], Pour-El and Richards asked, "What is the connection between the computability of the original nonlinear operator and the linear operator which results from it?" Yet at present, systematic studies of the issues raised by this question seem to be missing from the literature. In this paper, we study one problem in this direction: the Hartman-Grobman linearization theorem for ordinary differential equations (ODEs). We prove, roughly speaking, that near a hyperbolic equilibrium point x(0) of a nonlinear ODE (x) over dot = f(x), there is a computable homeomorphism H such that H circle phi = L circle H, where phi is the solution to the ODE and L is the solution to its linearization (x) over dot = Df (x(0)) x. (C) 2012 Elsevier B.V. All rights reserved.
dc.description.sponsorshipFundacao para a Ciencia e a Tecnologia; EU FEDER POCTI/POCI via SQIG - Instituto de Telecomunicacoes through the FCT [PEst-OE/EEI/LA0008/2011]
dc.identifier.doi10.1016/j.tcs.2012.07.013
dc.identifier.issn0304-3975
dc.identifier.issn1879-2294
dc.identifier.urihttp://hdl.handle.net/10400.1/11880
dc.language.isoeng
dc.peerreviewedyes
dc.publisherElsevier
dc.relationStrategic Project - LA 8 - 2011-2012
dc.subjectDifferential equations
dc.subjectSystems
dc.titleThe connection between computability of a nonlinear problem and its linearization: the Hartman-Grobman theorem revisited
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleStrategic Project - LA 8 - 2011-2012
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/PEst-OE%2FEEI%2FLA0008%2F2011/PT
oaire.citation.endPage110
oaire.citation.startPage101
oaire.citation.titleTheoretical Computer Science
oaire.citation.volume457
oaire.fundingStream6817 - DCRRNI ID
person.familyNameGraça
person.givenNameDaniel
person.identifier.ciencia-id2D11-56DE-3F11
person.identifier.orcid0000-0002-0330-833X
person.identifier.ridD-2335-2011
person.identifier.scopus-author-id8882791800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
rcaap.typearticle
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relation.isAuthorOfPublication.latestForDiscoveryba0c1461-5d2d-4f06-b648-df4a1a505bdf
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