Dynamic properties of the dynamical system SFnm(X), SFnm(f))

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dc.contributor.authorBarragán, Francoes_ES
dc.contributor.authorSantiago-Santos, Aliciaes_ES
dc.contributor.authorTenorio, Jesús F.es_ES
dc.contributor.funderSecretaría de Educación Pública, Méxicoes_ES
dc.date.accessioned2020-04-27T09:01:00Z
dc.date.available2020-04-27T09:01:00Z
dc.date.issued2020-04-03
dc.description.abstract[EN] Let X be a continuum and let n be a positive integer. We consider the hyperspaces Fn(X) and SFn(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFnm(X). For a given map f : X → X, we consider the induced maps Fn(f) : Fn(X) → Fn(X), SFn(f) : SFn(X) → SFn(X) and SFnm(f) : SFnm(X) → SFnm(X). In this paper, we introduce the dynamical system (SFnm(X), SFnm (f)) and we investigate some relationships between the dynamical systems (X, f), (Fn(X), Fn(f)), (SFn(X), SFn(f)) and (SFnm(X), SFnm(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.en_EN
dc.description.accrualMethodOJSes_ES
dc.description.bibliographicCitationBarragán, F.; Santiago-Santos, A.; Tenorio, JF. (2020). Dynamic properties of the dynamical system SFnm(X), SFnm(f)). Applied General Topology. 21(1):17-34. https://doi.org/10.4995/agt.2020.11807es_ES
dc.description.issue1es_ES
dc.description.referencesG. Acosta, A. Illanes and H. Méndez-Lango, The transitivity of induced maps, Topology Appl. 156, no. 5 (2009), 1013-1033. https://doi.org/10.1016/j.topol.2008.12.025es_ES
dc.description.referencesE. Akin, The General Topology of Dynamical Systems, Grad. Stud. Math., vol. 1, Amer. Math. Soc., Providence, 1993.es_ES
dc.description.referencesJ. Banks, Chaos for induced hyperspace maps, Chaos Solitons Fractals 25, no. 3 (2005), 681-685. https://doi.org/10.1016/j.chaos.2004.11.089es_ES
dc.description.referencesF. Barragán, On the n-fold symmetric product suspensions of a continuum, Topology Appl. 157, no. 3 (2010), 597-604. https://doi.org/10.1016/j.topol.2009.10.017es_ES
dc.description.referencesF. Barragán, Induced maps on n-fold symmetric product suspensions, Topology Appl. 158, no. 10 (2011), 1192-1205. https://doi.org/10.1016/j.topol.2011.04.006es_ES
dc.description.referencesF. Barragán, Aposyndetic properties of the n-fold symmetric product suspensions of a continuum, Glas. Mat. Ser. III 49(69), no. 1 (2014), 179-193. https://doi.org/10.3336/gm.49.1.13es_ES
dc.description.referencesF. Barragán, S. Macías and J. F. Tenorio, More on induced maps on n-fold symmetric product suspensions, Glas. Mat. Ser. III 50(70), no. 2 (2015), 489-512. https://doi.org/10.3336/gm.50.2.15es_ES
dc.description.referencesF. Barragán, A. Santiago-Santos and J. F. Tenorio, Dynamic properties for the induced maps on n-fold symmetric product suspensions, Glas. Mat. Ser. III 51(71), no. 2 (2016), 453-474.es_ES
dc.description.referencesW. Bauer and K. Sigmund, Topological dynamics of transformations induced on the space of probability measures, Monatsh. Math. 79 (1975), 81-92. https://doi.org/10.1007/BF01585664es_ES
dc.description.referencesG. D. Birkhoff, Dynamical Systems, American Math. Soc., Colloquium Publication., Vol. IX, Amer. Math. Soc. Providence, R. I., 1927.es_ES
dc.description.referencesK. Borsuk and S. Ulam, On symmetric products of topological space, Bull. Amer. Math. Soc. 37, no. 12 (1931), 875-882. https://doi.org/10.1090/S0002-9904-1931-05290-3es_ES
dc.description.referencesJ. Camargo, C. García and A. Ramírez, Transitivity of the Induced Map $C_n(f)$, Rev. Colombiana Mat. 48, no. 2 (2014), 235-245. https://doi.org/10.15446/recolma.v48n2.54131es_ES
dc.description.referencesJ. S. Cánovas-Peña and G. Soler-López, Topological entropy for induced hyperspace maps, Chaos Solitons Fractals 28, no. 4 (2006), 979-982. https://doi.org/10.1016/j.chaos.2005.08.173es_ES
dc.description.referencesE. Castañeda-Alvarado and J. Sánchez-Martínez, On the unicoherence of $F_n(X)$ and $SF^n_m(X)$ of continua, Topology Proc. 42 (2013), 309-326.es_ES
dc.description.referencesE. Castañeda-Alvarado, F. Orozco-Zitli and J. Sánchez-Martínez, Induced mappings between quotient spaces of symmetric products of continua, Topology Appl. 163 (2014), 66-76. https://doi.org/10.1016/j.topol.2013.10.007es_ES
dc.description.referencesJ. Dugundji, Topology, Boston, London, Sydney, Toronto: Allyn and Bacon, Inc, 1966.es_ES
dc.description.referencesL. Fernández and C. Good, Shadowing for induced maps of hyperspaces, Fund. Math. 235, no. 3 (2016), 277-286. https://doi.org/10.4064/fm136-2-2016es_ES
dc.description.referencesJ. L. Gómez-Rueda, A. Illanes and H. Méndez-Lango, Dynamic properties for the induced maps in the symmetric products, Chaos Solitons Fractals 45, no. 9-10 (2012), 1180-1187. https://doi.org/10.1016/j.chaos.2012.05.003es_ES
dc.description.referencesG. Higuera and A. Illanes, Induced mappings on symmetric products, Topolology Proc. 37 (2011), 367-401.es_ES
dc.description.referencesA. Illanes and S. B. Nadler, Jr., Hyperspaces: fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, New York, Basel, 1999.es_ES
dc.description.referencesS. Kolyada, L. Snoha and S. Trofimchuk, Noninvertible minimal maps, Fund. Math. 168, no. 2 (2001), 141-163. https://doi.org/10.4064/fm168-2-5es_ES
dc.description.referencesD. Kwietniak, Exact Devaney chaos and entropy, Qual. Theory Dyn. Syst. 6, no. 1 (2005), 169-179. https://doi.org/10.1007/BF02972670es_ES
dc.description.referencesD. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals 33, no. 1 (2007), 76-86. https://doi.org/10.1016/j.chaos.2005.12.033es_ES
dc.description.referencesG. Liao, L. Wang and Y. Zhang, Transitivity, mixing and chaos for a class of set-valued mappings, Sci. China Ser. A 49, no. 1 (2006), 1-8. https://doi.org/10.1007/s11425-004-5234-5es_ES
dc.description.referencesX. Ma, B. Hou and G. Liao, Chaos in hyperspace system, Chaos Solitons Fractals 40, no. 2 (2009), 653-660. https://doi.org/10.1016/j.chaos.2007.08.009es_ES
dc.description.referencesJ. C. Macías, On n-fold pseudo-hyperspace suspensions of continua, Glas. Mat. Ser. III 43(63), no. 2 (2008), 439-449. https://doi.org/10.3336/gm.43.2.14es_ES
dc.description.referencesS. Macías, On the n-fold hyperspaces suspension of continua, Topology Appl. 138, no. 1-3 (2004), 125-138. https://doi.org/10.1016/j.topol.2003.08.023es_ES
dc.description.referencesS. Macías, Topics on Continua, Pure and Applied Mathematics Series, Vol. 275, Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York, Singapore, 2005.es_ES
dc.description.referencesS. B. Nadler, Jr., A fixed point theorem for hyperspaces suspensions, Houston J. Math. 5, no. 1 (1979), 125-132.es_ES
dc.description.referencesS. B. Nadler, Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, New York, Basel, 1978. Reprinted in: Aportaciones Matemáticas de la Sociedad Matemática Mexicana, Serie Textos #33, 2006.es_ES
dc.description.referencesA. Peris, Set-valued discrete chaos, Chaos Solitons Fractals 26, no. 1 (2005), 19-23. https://doi.org/10.1016/j.chaos.2004.12.039es_ES
dc.description.referencesH. Román-Flores, A note on transitivity in set-valued discrete systems, Chaos Solitons Fractals 17, no. 1 (2003), 99-104. https://doi.org/10.1016/S0960-0779(02)00406-Xes_ES
dc.description.referencesM. Sabbaghan and H. Damerchiloo, A note on periodic points and transitive maps, Math. Sci. Q. J. 5, no. 3 (2011), 259-266.es_ES
dc.description.referencesY. Wang and G. Wei, Characterizing mixing, weak mixing and transitivity on induced hyperspace dynamical systems, Topology Appl. 155, no. 1 (2007), 56-68. https://doi.org/10.1016/j.topol.2007.09.003es_ES
dc.description.sponsorshipThis paper was partially supported by the project: “Propiedades din´amicas y topol´ogicas sobre sistemas din´amicos inducidos”, (UTMIX-PTC-064) of PRODEP, 2017.es_ES
dc.description.upvformatpfin34es_ES
dc.description.upvformatpinicio17es_ES
dc.description.volume21es_ES
dc.identifier.doi10.4995/agt.2020.11807
dc.identifier.eissn1989-4147
dc.identifier.issn1576-9402
dc.identifier.urihttps://riunet.upv.es/handle/10251/141550
dc.languageIngléses_ES
dc.publisherUniversitat Politècnica de Valènciaes_ES
dc.relation.ispartofApplied General Topologyes_ES
dc.relation.pasarelaOJS\11807es_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/SEP//UTMIX-PTC-064/es_ES
dc.relation.publisherversionhttps://doi.org/10.4995/agt.2020.11807es_ES
dc.relation.references10.1016/j.topol.2008.12.025es_ES
dc.relation.references10.1016/j.chaos.2004.11.089es_ES
dc.relation.references10.1016/j.topol.2009.10.017es_ES
dc.relation.references10.1016/j.topol.2011.04.006es_ES
dc.relation.references10.3336/gm.49.1.13es_ES
dc.relation.references10.3336/gm.50.2.15es_ES
dc.relation.references10.1007/BF01585664es_ES
dc.relation.references10.1090/S0002-9904-1931-05290-3es_ES
dc.relation.references10.15446/recolma.v48n2.54131es_ES
dc.relation.references10.1016/j.chaos.2005.08.173es_ES
dc.relation.references10.1016/j.topol.2013.10.007es_ES
dc.relation.references10.4064/fm136-2-2016es_ES
dc.relation.references10.1016/j.chaos.2012.05.003es_ES
dc.relation.references10.4064/fm168-2-5es_ES
dc.relation.references10.1007/BF02972670es_ES
dc.relation.references10.1016/j.chaos.2005.12.033es_ES
dc.relation.references10.1007/s11425-004-5234-5es_ES
dc.relation.references10.1016/j.chaos.2007.08.009es_ES
dc.relation.references10.3336/gm.43.2.14es_ES
dc.relation.references10.1016/j.topol.2003.08.023es_ES
dc.relation.references10.1016/j.chaos.2004.12.039es_ES
dc.relation.references10.1016/S0960-0779(02)00406-Xes_ES
dc.relation.references10.1016/j.topol.2007.09.003es_ES
dc.rightsReconocimiento - No comercial - Sin obra derivada (by-nc-nd)es_ES
dc.rights.accessRightsAbiertoes_ES
dc.subjectChaotices_ES
dc.subjectContinuumes_ES
dc.subjectDynamical systemes_ES
dc.subjectExactes_ES
dc.subjectFeebly openes_ES
dc.subjectHyperspacees_ES
dc.subjectInduced mapes_ES
dc.subjectIrreduciblees_ES
dc.subjectMixinges_ES
dc.subjectStrongly transitivees_ES
dc.subjectSymmetric productes_ES
dc.subjectSymmetric product suspensiones_ES
dc.subjectTotally transitivees_ES
dc.subjectTransitivees_ES
dc.subjectTurbulentes_ES
dc.subjectWeakly mixinges_ES
dc.titleDynamic properties of the dynamical system SFnm(X), SFnm(f))es_ES
dc.typeArtículoes_ES
dc.type.versioninfo:eu-repo/semantics/publishedVersiones_ES
dspace.entity.typePublication
upv.uuid0f8c8ea9-82a0-4b9e-aa1a-2c40cf38fe8ees_ES

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Applied General Topology - Vol 21, No 1 (2020)