- -

Chaotic Behaviour on Invariant Sets of Linear Operators

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Chaotic Behaviour on Invariant Sets of Linear Operators

Show full item record

Murillo Arcila, M.; Peris Manguillot, A. (2015). Chaotic Behaviour on Invariant Sets of Linear Operators. Integral Equations and Operator Theory. 81(4):483-497. doi:10.1007/s00020-014-2188-z

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/72432

Files in this item

Item Metadata

Title: Chaotic Behaviour on Invariant Sets of Linear Operators
Author:
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Universitat Politècnica de València. Escuela Técnica Superior de Arquitectura - Escola Tècnica Superior d'Arquitectura
Issued date:
Abstract:
We study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, our purpose is to ...[+]
Subjects: Hypercyclic operators , Invariant sets , Topological mixing , Devaney chaos , Mixing measures
Copyrigths: Cerrado
Source:
Integral Equations and Operator Theory. (issn: 0378-620X )
DOI: 10.1007/s00020-014-2188-z
Publisher:
Springer Verlag (Germany)
Publisher version: http://dx.doi.org/10.1007/s00020-014-2188-z
Thanks:
This work is supported in part by MICINN and FEDER, Projects MTM2010-14909 and MTM2013-47093-P, and by GVA, Project PROMETEOII/2013/013. The first author is supported by a Grant from the FPU Program of MEC.
Type: Artículo

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)

Aroza J., Peris A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18, 647–655 (2012)

Banasiak J., Moszyński M.: A generalization of Desch-Schappacher-Webb criteria for chaos. Discret. Contin. Dyn. Syst. 12, 959–972 (2005) [+]
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)

Aroza J., Peris A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18, 647–655 (2012)

Banasiak J., Moszyński M.: A generalization of Desch-Schappacher-Webb criteria for chaos. Discret. Contin. Dyn. Syst. 12, 959–972 (2005)

Banasiak J., Moszyński M.: Dynamics of birth-and-death processes with proliferation—stability and chaos. Discret. Contin. Dyn. Syst. 29, 67–79 (2011)

Bartoll S., Martínez-Giménez F., Peris A.: The specification property for backward shifts. J. Differ. Equ. Appl. 18, 599–605 (2012)

Bauer W., Sigmund K.: Topological dynamics of transformations induced on the space of probability measures. Monatsh. Math. 79, 81–92 (1975)

Bayart F., Grivaux S.: Hypercyclicity and unimodular point spectrum. J. Funct. Anal. 226, 281–300 (2005)

Bayart F., Matheron É.: Dynamics of Linear Operators. Cambridge University Press, Cambridge (2009)

Bayart, F., Matheron, É.: Mixing operators and small subsets of the circle. J. Reine Angew. Math. (2014). doi: 10.1515/crelle-2014-0002

Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors. Ergod. Theory Dyn. Syst. 27, 383–404 (2007). Erratum: Ergod. Theory Dyn. Systems 29, 1993–1994 (2009)

Bonet J., Frerick L., Peris A., Wengenroth J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)

Devaney, R.L.: An Introduction to Chaotic Dynamical Systems. Benjamin/Cummings, Menlo Park, CA, (1986); second edition, Addison-Wesley, Redwood City (1989)

Dineen S.: Complex Analysis on Infinite-Dimensional Spaces. Springer, London (1999)

Einsiedler M., Ward T.: Ergodic Theory with a View Towards Number Theory, Volume 259 of Graduate Texts in Mathematics. Springer-Verlag London Ltd., London (2011)

Feldman, N. S.: Linear chaos? http://home.wlu.edu/~feldmann/research.html (2001)

Flytzanis E.: Unimodular eigenvalues and linear chaos in Hilbert spaces. Geom. Funct. Anal. 5, 1–13 (1995)

Furstenberg H.: Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Syst. Theory 1, 1–49 (1967)

Glasner E.: Classifying dynamical systems by their recurrence properties. Topol. Methods Nonlinear Anal. 24, 21–40 (2004)

Godefroy G., Kalton N.J.: Lipschitz-free Banach spaces. Studi. Math. 159, 121–141 (2003)

Grivaux S.: Hypercyclic operators, mixing operators, and the bounded steps problem. J. Oper. Theory 54, 147–168 (2005)

Grivaux S., Matheron E.: Invariant measures for frequently hypercyclic operators. Adv. Math. 265, 371–427 (2014)

Grosse-Erdmann K.G., Peris A.: Weakly mixing operators on topological vector spaces. Rev. R. Acad. Cienc. Exactas Fí s. Nat. Ser. A Mat. RACSAM 104, 413–426 (2010)

Grosse-Erdmann K.G., Peris Manguillot A.: Linear chaos. Universitext. Springer-Verlag London Ltd, London (2011)

Kalton N.J.: The nonlinear geometry of Banach spaces. Rev. Math. Complut. 21, 7–60 (2008)

Mangino E., Peris A.: Frequently hypercyclic semigroups. Studi. Math. 202, 227–242 (2011)

Matsui M., Takeo F.: Chaotic semigroups generated by certain differential operators of order 1. SUT J. Math. 37, 51–67 (2001)

Murillo-Arcila M., Peris A.: Mixing properties for nonautonomous linear dynamics and invariant sets. Appl. Math. Lett. 26, 215–218 (2013)

Murillo-Arcila M., Peris A.: Strong mixing measures for linear operators and frequent hypercyclicity. J. Math. Anal. Appl. 398, 462–465 (2013)

Murillo-Arcila, M., Peris, A.: Strong mixing measures for C 0-semigroups. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM (2014). doi: 10.1007/s13398-014-0169-3

Protopopescu, V.: Linear vs nonlinear and infinite vs finite: an interpretation of chaos, Oak Ridge National Laboratory Report TM-11667, Oak Ridge, TN, (1990)

Schaefer H.H.: Topological Vector Spaces. Graduate Texts in Mathematics, Vol. 3. Springer, New York (1971)

Shkarin S.: Hypercyclic operators on topological vector spaces. J. Lond. Math. Soc. 86, 195–213 (2012)

Takeo F.: Chaos and hypercyclicity for solution semigroups to some partial differential equations. Nonlinear Anal. 63, 1943–1953 (2005)

Walters P.: An Introduction to Ergodic Theory. Springer, New York (1982)

[-]

This item appears in the following Collection(s)

Show full item record