Global linearization without hyperbolicity

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dc.contributor.authorKvalheim, Matthew D.
dc.contributor.authorSontag, Eduardo D.
dc.date.accessioned2025-04-01T14:55:58Z
dc.date.available2025-04-01T14:55:58Z
dc.date.issued2025-02-13
dc.description.abstractWe give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjugacy is (i) defined on the entire basin of attraction if the vector field is complete, and (ii) a C superscript (k ≥ 1) diffeomorphism on the complement of the equilibrium if the vector field is C (superscript k) and the underlying space is not 5-dimensional. We also show that the C (superscript k) statement in the 5-dimensional case is equivalent to the 4-dimensional smooth Poincaré conjecture.
dc.description.sponsorshipThis material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-24-1-0299 to Kvalheim and award number AFOSR FA9550-21-1-0289 to Sontag.
dc.description.urihttp://arxiv.org/abs/2502.07708
dc.format.extent7 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifierdoi:10.13016/m2vs71-cdqf
dc.identifier.urihttps://doi.org/10.48550/arXiv.2502.07708
dc.identifier.urihttp://hdl.handle.net/11603/37947
dc.language.isoen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
dc.rightsPublic Domain
dc.rights.urihttps://creativecommons.org/publicdomain/mark/1.0/
dc.subjectMathematics - Dynamical Systems
dc.subjectComputer Science - Systems and Control
dc.subjectElectrical Engineering and Systems Science - Systems and Control
dc.titleGlobal linearization without hyperbolicity
dc.typeText
dcterms.creatorhttps://orcid.org/0000-0002-2662-6760

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