On the stability of generalized hyperbolic operators

dc.contributor.authorBernardes-Junior, Nilson Da Costaes_ES
dc.contributor.funderAgencia Estatal de Investigaciónes_ES
dc.contributor.funderCoordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, Brasiles_ES
dc.contributor.funderConselho Nacional de Desenvolvimento Científico e Tecnológico, Brasiles_ES
dc.date.accessioned2026-05-06T09:23:42Z
dc.date.available2026-05-06T09:23:42Z
dc.date.issued2026-03-11es_ES
dc.description.abstract[EN] Our main goal is to prove that every invertible generalized hyperbolic operator on a Banach space has a stability property, known as time-dependent stability, which was introduced by J. M. Franks (Invent. Math. 24 (1974), 163-172) and is stronger than structural stability.es_ES
dc.description.accrualMethodSes_ES
dc.description.bibliographicCitationBernardes-Junior, NDC. (2026). On the stability of generalized hyperbolic operators. Revista Matemática Complutense. https://doi.org/10.1007/s13163-026-00569-5es_ES
dc.description.referencesAndronov, A., Pontrjagin, L.: Structurally stable systems. Dokl. Akad. Nauk SSSR 14, 247–250 (1937). ((Russian))es_ES
dc.description.referencesBayart, F.: Two problems on weighted shifts in linear dynamics. Proc. Amer. Math. Soc. 149(12), 5255–5266 (2021)es_ES
dc.description.referencesBernardes, N.C., Jr., Caraballo, B.M., Darji, U.B., Fávaro, V.V., Peris, A.: Generalized hyperbolicity, stability and expansivity for operators on locally convex spaces. J. Funct. Anal. 288(2), 110696 (2025). (51 pp)es_ES
dc.description.referencesBernardes, N.C., Jr., Cirilo, P.R., Darji, U.B., Messaoudi, A., Pujals, E.R.: Expansivity and shadowing in linear dynamics. J. Math. Anal. Appl. 461(1), 796–816 (2018)es_ES
dc.description.referencesBernardes, N.C., Jr., Messaoudi, A.: A generalized Grobman-Hartman theorem. Proc. Amer. Math. Soc. 148(10), 4351–4360 (2020)es_ES
dc.description.referencesBernardes, N.C., Jr., Messaoudi, A.: Shadowing and structural stability for operators. Ergodic Theory Dynam. Systems 41(4), 961–980 (2021)es_ES
dc.description.referencesBernardes, N.C., Jr., Peris, A.: On shadowing and chain recurrence in linear dynamics. Adv. Math. 441, 109539 (2024). (46 pp)es_ES
dc.description.referencesCirilo, P.R., Gollobit, B., Pujals, E.R.: Dynamics of generalized hyperbolic linear operators. Adv. Math. 387, 107830 (2021). (37 pp)es_ES
dc.description.referencesFranks, J.M.: Absolutely structurally stable diffeomorphisms. Proc. Amer. Math. Soc. 37, 293–296 (1973)es_ES
dc.description.referencesFranks, J.M.: Time dependent stable diffeomorphisms. Invent. Math. 24, 163–172 (1974)es_ES
dc.description.referencesGranas, A., Dugundji, J.: Fixed Point Theory. Springer-Verlag, New York (2003)es_ES
dc.description.referencesGuckenheimer, J.: Absolutely $$\Omega $$-stable diffeomorphisms. Topology 11, 195–197 (1972)es_ES
dc.description.referencesGuckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Revised and corrected reprint of the 1983 original, Applied Mathematical Sciences, 42. Springer-Verlag, New York (1990)es_ES
dc.description.referencesHartman, P.: A lemma in the theory of structural stability of differential equations. Proc. Amer. Math. Soc. 11, 610–620 (1960)es_ES
dc.description.referencesKatok, A., Hasselblatt, B.: Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, Cambridge (1995)es_ES
dc.description.referencesLee, K., Morales Rojas, C.A.: Topological stability, $$L$$-shadowing and generalized hyperbolicity. Tunisian J. Math. 6(3), 549–570 (2024)es_ES
dc.description.referencesLenarduzzi, F., Messaoudi, A.: Stability of non-invertible operators on Banach spaces. Proc. Amer. Math. Soc. 153(9), 3781–3794 (2025)es_ES
dc.description.referencesMelo, W., Palis, J.: Geometric Theory of Dynamical Systems - An Introduction. Springer-Verlag, New York (1982)es_ES
dc.description.referencesMoser, J.K.: On a theorem of Anosov. J. Differential Equations 5, 411–440 (1969)es_ES
dc.description.referencesPalis, J.: On the local structure of hyperbolic points in Banach spaces. An. Acad. Brasil. Ci. 40, 263–266 (1968)es_ES
dc.description.referencesPugh, C.C.: On a theorem of P. Hartman. Amer. J. Math. 91, 363–367 (1969)es_ES
dc.description.referencesRobbin, J.W.: Topological conjugacy and structural stability for discrete dynamical systems. Bull. Amer. Math. Soc. 78(6), 923–952 (1972)es_ES
dc.description.referencesShub, M.: Global Stability of Dynamical Systems (with the collaboration of A. Fathi and R. Langevin), Springer-Verlag, New York (1987)es_ES
dc.description.referencesWalters, P.: Anosov diffeomorphisms are topologically stable. Topology 9, 71–78 (1970)es_ES
dc.description.sponsorshipThe author is beneficiary of a grant within the framework of the grants for the retraining, modality María Zambrano, in the Spanish university system (Spanish Ministry of Universities, financed by the European Union, NextGenerationEU). The author was also partially supported by CNPq Project #308238/2021-4, by CAPES Finance Code 001, and by MCIN/AEI/10.13039/501100011033/FEDER, UE, Project PID2022-139449NB-I00.es_ES
dc.identifier.doi10.1007/s13163-026-00569-5es_ES
dc.identifier.issn1139-1138es_ES
dc.identifier.urihttps://riunet.upv.es/handle/10251/234919
dc.languageIngléses_ES
dc.publisherSpringer-Verlages_ES
dc.relation.ispartofRevista Matemática Complutensees_ES
dc.relation.pasarelaS\580083es_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-139449NB-I00/ES/DINAMICA DE OPERADORES Y ECUACIONES DE EVOLUCION/es_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/CNPq//308238%2F2021-4/es_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/CAPES//001/es_ES
dc.relation.publisherversionhttps://doi.org/10.1007/s13163-026-00569-5es_ES
dc.rightsReconocimiento (by)es_ES
dc.rights.accessRightsAbiertoes_ES
dc.subjectHyperbolicityes_ES
dc.subjectGeneralized hyperbolicityes_ES
dc.subjectStructural stabilityes_ES
dc.subjectTime-dependent stabilityes_ES
dc.subjectLinear operatorses_ES
dc.subjectBanach spaceses_ES
dc.titleOn the stability of generalized hyperbolic operatorses_ES
dc.typeArtículoes_ES
dc.type.versioninfo:eu-repo/semantics/publishedVersiones_ES
dspace.entity.typePublication
upv.uuid40cfb797-567e-413e-bdfd-ffae7de26e0des_ES

Archivos

Bloque original

Mostrando 1 - 1 de 1
Cargando...
Miniatura
Nombre:
Bernardes-Junior - On the stability of generalized hyperbolic operators.pdf
Tamaño:
326.32 KB
Formato:
Adobe Portable Document Format
Descripción:
Versión editorial