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The Specification Property for C0-Semigroups

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The Specification Property for C0-Semigroups

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dc.contributor.author Bartoll Arnau, Salud es_ES
dc.contributor.author Martínez Jiménez, Félix es_ES
dc.contributor.author Peris Manguillot, Alfredo es_ES
dc.contributor.author Ródenas Escribá, Francisco De Asís es_ES
dc.date.accessioned 2021-01-19T04:31:51Z
dc.date.available 2021-01-19T04:31:51Z
dc.date.issued 2019-06 es_ES
dc.identifier.issn 1660-5446 es_ES
dc.identifier.uri http://hdl.handle.net/10251/159337
dc.description.abstract [EN] We study one of the strongest versions of chaos for continuous dynamical systems, namely the specification property. We extend the definition of specification property for operators on a Banach space to strongly continuous one-parameter semigroups of operators, that is, C0-semigroups. In addition, we study the relationships of the specification property for C0-semigroups (SgSP) with other dynamical properties: mixing, Devaney's chaos, distributional chaos, and frequent hypercyclicity. Concerning the applications, we provide several examples of semigroups which exhibit the SgSP with particular interest on solution semigroups to certain linear PDEs, which range from the hyperbolic heat equation to the Black-Scholes equation. es_ES
dc.description.sponsorship The authors were supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P. The second and third authors were also supported by Generalitat Valenciana, Projects PROMETEOII/2013/013 and PROMETEO/2017/102. We are indebted to the referee whose valuable comments produced an improvement in the presentation of the paper. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Mediterranean Journal of Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Hypercyclic semigroups of operators es_ES
dc.subject Specification property es_ES
dc.subject Frequently hypercyclic semigroups of operators es_ES
dc.subject Chaotic semigroups of operators es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title The Specification Property for C0-Semigroups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00009-019-1353-7 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2013-47093-P/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bartoll Arnau, S.; Martínez Jiménez, F.; Peris Manguillot, A.; Ródenas Escribá, FDA. (2019). The Specification Property for C0-Semigroups. Mediterranean Journal of Mathematics. 16(3):1-12. https://doi.org/10.1007/s00009-019-1353-7 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00009-019-1353-7 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 12 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 16 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\393696 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references Albanese, A.A., Barrachina, X., Mangino, E.M., Peris, A.: Distributional chaos for strongly continuous semigroups of operators. Commun. Pure Appl. Anal. 12, 2069–2082 (2013) es_ES
dc.description.references Aroza, J., Kalmes, T., Mangino, E.: Chaotic $$C_0$$-semigroups induced by semiflows in Lebesgue and Sobolev spaces. J. Math. Anal. Appl. 412, 77–98 (2014) es_ES
dc.description.references Badea, C., Grivaux, S.: Unimodular eigenvalues, uniformly distributed sequences and linear dynamics. Adv. Math. 211, 766–793 (2007) es_ES
dc.description.references Banasiak, J., Moszyński, M.: Dynamics of birth-and-death processes with proliferation-stability and chaos. Discrete Contin. Dyn. Syst. 29, 67–79 (2011) es_ES
dc.description.references Bartoll, S., Martínez-Giménez, F., Peris, A.: The specification property for backward shifts. J. Differ. Equ. Appl. 18, 599–605 (2012) es_ES
dc.description.references Bartoll, S., Martínez-Giménez, F., Peris, A.: Operators with the specification property. J. Math. Anal. Appl. 436, 478–488 (2016) es_ES
dc.description.references Bayart, F., Bermúdez, T.: Semigroups of chaotic operators. Bull. Lond. Math. Soc. 41, 823–830 (2009) es_ES
dc.description.references Bayart, F., Grivaux, S.: Frequently hypercyclic operators. Trans. Am. Math. Soc. 358, 5083–5117 (2006) es_ES
dc.description.references Bayart, F., Matheron, É.: Dynamics of Linear Operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009) es_ES
dc.description.references Bayart, F., Ruzsa, I.Z.: Difference sets and frequently hypercyclic weighted shifts. Ergod. Theory Dyn. Syst. 35, 691–709 (2015) es_ES
dc.description.references Bermúdez, T., Bonilla, A., Conejero, J.A., Peris, A.: Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Stud. Math. 170, 57–75 (2005) es_ES
dc.description.references Bernardes Jr., N.C., Bonilla, A., Müller, V., Peris, A.: Distributional chaos for linear operators. J. Funct. Anal. 265, 2143–2163 (2013) es_ES
dc.description.references Bernardes Jr., N.C., Bonilla, A., Müller, V., Peris, A.: Li–Yorke chaos in linear dynamics. Ergod. Theory Dyn. Syst. 35, 1723–1745 (2015) es_ES
dc.description.references Bernardes Jr., N.C., Bonilla, A., Peris, A., Wu, X.: Distributional chaos for operators on Banach spaces. J. Math. Anal. Appl. 459, 797–821 (2018) es_ES
dc.description.references Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors. Ergod. Theory Dyn. Syst. 27, 383–404 (2007) es_ES
dc.description.references Bowen, R.: Topological entropy and axiom $${\rm A}$$. In: Global Analysis (Proc. Sympos. Pure Math., vol. XIV, Berkeley, Calif., 1968), pp. 23–41. Amer. Math. Soc., Providence (1970) es_ES
dc.description.references Bowen, R.: Periodic orbits for hyperbolic flows. Am. J. Math. 94, 1–30 (1972) es_ES
dc.description.references Chakir, M., EL Mourchid, S.: Strong mixing Gaussian measures for chaotic semigroups. J. Math. Anal. Appl. 459, 778–788 (2018) es_ES
dc.description.references Conejero, J.A., Lizama, C., Murillo-Arcila, M., Peris, A.: Linear dynamics of semigroups generated by differential operators. Open Math. 15, 745–767 (2017) es_ES
dc.description.references Conejero, J.A., Müller, V., Peris, A.: Hypercyclic behaviour of operators in a hypercyclic $$C_0$$-semigroup. J. Funct. Anal. 244, 342–348 (2007) es_ES
dc.description.references Conejero, J.A., Peris, A.: Hypercyclic translation $$C_0$$-semigroups on complex sectors. Discrete Contin. Dyn. Syst. 25, 1195–1208 (2009) es_ES
dc.description.references Conejero, J.A., Peris, A., Trujillo, M.: Chaotic asymptotic behaviour of the hyperbolic heat transfer equation solutions. Int. J. Bifur. Chaos Appl. Sci. Eng. 20, 2943–2947 (2010) es_ES
dc.description.references Costakis, G., Peris, A.: Hypercyclic semigroups and somewhere dense orbits. C. R. Math. Acad. Sci. Paris 335, 895–898 (2002) es_ES
dc.description.references Desch, W., Schappacher, W., Webb, G.F.: Hypercyclic and chaotic semigroups of linear operators. Ergod. Theory Dyn. Syst. 17, 793–819 (1997) es_ES
dc.description.references Emamirad, H., Goldstein, G., Goldstein, J.A.: Chaotic solution for the Black–Scholes equation. Proc. Am. Math. Soc. 140, 2043–2052 (2012) es_ES
dc.description.references Goldstein, J.A., Mininni, R.M., Romanelli, S.: A new explicit formula for the solution of the Black–Merton–Scholes equation. In: Infinite Dimensional Stochastic Analysis, World Series Publ., pp. 226–235 (2008) es_ES
dc.description.references Grosse-Erdmann, K.G., Peris, A.: Linear Chaos. Universitext, Springer-Verlag London Ltd., London (2011) es_ES
dc.description.references Herzog, G.: On a universality of the heat equation. Math. Nachr. 188, 169–171 (1997) es_ES
dc.description.references Mangino, E.M., Peris, A.: Frequently hypercyclic semigroups. Stud. Math. 202, 227–242 (2011) es_ES
dc.description.references Mangino, E.M., Murillo-Arcila, M.: Frequently hypercyclic translation semigroups. Stud. Math. 227, 219–238 (2015) es_ES
dc.description.references Murillo-Arcila, M., Peris, A.: Strong mixing measures for $$C_0$$-semigroups. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 109, 101–115 (2015) es_ES
dc.description.references Oprocha, P.: Specification properties and dense distributional chaos. Discrete Contin. Dyn. Syst. 17, 821–833 (2007) es_ES
dc.description.references Rudnicki, R.: Chaoticity and invariant measures for a cell population model. J. Math. Anal. Appl. 339, 151–165 (2012) es_ES
dc.description.references Yin, Z., Wei, Y.: Recurrence and topological entropy of translation operators. J. Math. Anal. Appl. 460, 203–215 (2018) es_ES


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