On the stability of generalized hyperbolic operators
| dc.contributor.author | Bernardes-Junior, Nilson Da Costa | es_ES |
| dc.contributor.funder | Agencia Estatal de Investigación | es_ES |
| dc.contributor.funder | Coordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, Brasil | es_ES |
| dc.contributor.funder | Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brasil | es_ES |
| dc.date.accessioned | 2026-05-06T09:23:42Z | |
| dc.date.available | 2026-05-06T09:23:42Z | |
| dc.date.issued | 2026-03-11 | es_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.accrualMethod | S | es_ES |
| dc.description.bibliographicCitation | Bernardes-Junior, NDC. (2026). On the stability of generalized hyperbolic operators. Revista Matemática Complutense. https://doi.org/10.1007/s13163-026-00569-5 | es_ES |
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| dc.description.references | Bernardes, 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.references | Bernardes, 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.references | Bernardes, N.C., Jr., Messaoudi, A.: A generalized Grobman-Hartman theorem. Proc. Amer. Math. Soc. 148(10), 4351–4360 (2020) | es_ES |
| dc.description.references | Bernardes, N.C., Jr., Messaoudi, A.: Shadowing and structural stability for operators. Ergodic Theory Dynam. Systems 41(4), 961–980 (2021) | es_ES |
| dc.description.references | Bernardes, N.C., Jr., Peris, A.: On shadowing and chain recurrence in linear dynamics. Adv. Math. 441, 109539 (2024). (46 pp) | es_ES |
| dc.description.references | Cirilo, P.R., Gollobit, B., Pujals, E.R.: Dynamics of generalized hyperbolic linear operators. Adv. Math. 387, 107830 (2021). (37 pp) | es_ES |
| dc.description.references | Franks, J.M.: Absolutely structurally stable diffeomorphisms. Proc. Amer. Math. Soc. 37, 293–296 (1973) | es_ES |
| dc.description.references | Franks, J.M.: Time dependent stable diffeomorphisms. Invent. Math. 24, 163–172 (1974) | es_ES |
| dc.description.references | Granas, A., Dugundji, J.: Fixed Point Theory. Springer-Verlag, New York (2003) | es_ES |
| dc.description.references | Guckenheimer, J.: Absolutely $$\Omega $$-stable diffeomorphisms. Topology 11, 195–197 (1972) | es_ES |
| dc.description.references | Guckenheimer, 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.references | Hartman, P.: A lemma in the theory of structural stability of differential equations. Proc. Amer. Math. Soc. 11, 610–620 (1960) | es_ES |
| dc.description.references | Katok, A., Hasselblatt, B.: Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, Cambridge (1995) | es_ES |
| dc.description.references | Lee, K., Morales Rojas, C.A.: Topological stability, $$L$$-shadowing and generalized hyperbolicity. Tunisian J. Math. 6(3), 549–570 (2024) | es_ES |
| dc.description.references | Lenarduzzi, F., Messaoudi, A.: Stability of non-invertible operators on Banach spaces. Proc. Amer. Math. Soc. 153(9), 3781–3794 (2025) | es_ES |
| dc.description.references | Melo, W., Palis, J.: Geometric Theory of Dynamical Systems - An Introduction. Springer-Verlag, New York (1982) | es_ES |
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| dc.description.references | Robbin, J.W.: Topological conjugacy and structural stability for discrete dynamical systems. Bull. Amer. Math. Soc. 78(6), 923–952 (1972) | es_ES |
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| dc.description.sponsorship | The 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.doi | 10.1007/s13163-026-00569-5 | es_ES |
| dc.identifier.issn | 1139-1138 | es_ES |
| dc.identifier.uri | https://riunet.upv.es/handle/10251/234919 | |
| dc.language | Inglés | es_ES |
| dc.publisher | Springer-Verlag | es_ES |
| dc.relation.ispartof | Revista Matemática Complutense | es_ES |
| dc.relation.pasarela | S\580083 | es_ES |
| dc.relation.projectID | info: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.projectID | info:eu-repo/grantAgreement/CNPq//308238%2F2021-4/ | es_ES |
| dc.relation.projectID | info:eu-repo/grantAgreement/CAPES//001/ | es_ES |
| dc.relation.publisherversion | https://doi.org/10.1007/s13163-026-00569-5 | es_ES |
| dc.rights | Reconocimiento (by) | es_ES |
| dc.rights.accessRights | Abierto | es_ES |
| dc.subject | Hyperbolicity | es_ES |
| dc.subject | Generalized hyperbolicity | es_ES |
| dc.subject | Structural stability | es_ES |
| dc.subject | Time-dependent stability | es_ES |
| dc.subject | Linear operators | es_ES |
| dc.subject | Banach spaces | es_ES |
| dc.title | On the stability of generalized hyperbolic operators | es_ES |
| dc.type | Artículo | es_ES |
| dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
| dspace.entity.type | Publication | |
| upv.uuid | 40cfb797-567e-413e-bdfd-ffae7de26e0d | es_ES |
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