- -

Distributional chaos for operators with full scrambled sets

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Distributional chaos for operators with full scrambled sets

Show full item record

Martínez Jiménez, F.; Oprocha, P.; Peris Manguillot, A. (2013). Distributional chaos for operators with full scrambled sets. Mathematische Zeitschrift. 274(1-2):603-612. https://doi.org/10.1007/s00209-012-1087-8

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/43593

Files in this item

Item Metadata

Title: Distributional chaos for operators with full scrambled sets
Author: Martínez Jiménez, Félix Oprocha, Piotr Peris Manguillot, Alfredo
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, ...[+]
Subjects: Distributional chaos , Hypercyclic operators , Irregular vectors
Copyrigths: Reserva de todos los derechos
Source:
Mathematische Zeitschrift. (issn: 0025-5874 ) (eissn: 1432-1823 )
DOI: 10.1007/s00209-012-1087-8
Publisher:
Springer Verlag (Germany)
Publisher version: http://dx.doi.org/10.1007/s00209-012-1087-8
Project ID:
info:eu-repo/grantAgreement/EC/FP7/272297/EU/Topological aspects of dynamical independence and chaos/
info:eu-repo/grantAgreement/MICINN//MTM2010-14909/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/
GV, Project PROMETEO/2008/101
Marie Curie European Reintegration Grant of the European Commission under grant agreement no. PERG08-GA-2010-272297
Thanks:
The research of first and third author was supported by MEC and FEDER, project MTM2010-14909 and by GV, Project PROMETEO/2008/101. The research of second author was supported by the Marie Curie European Reintegration Grant ...[+]
Type: Artículo

References

Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s definition of chaos. Am. Math. Monthly 99(4), 332–334 (1992)

Barrachina, X., Peris, A.: Distributionally chaotic translation semigroups. J. Differ. Equ. Appl. 18, 751–761 (2012)

Beauzamy, B.: Introduction to Operator Theory and Invariant Subspaces. North-Holland, Amsterdam (1988) [+]
Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s definition of chaos. Am. Math. Monthly 99(4), 332–334 (1992)

Barrachina, X., Peris, A.: Distributionally chaotic translation semigroups. J. Differ. Equ. Appl. 18, 751–761 (2012)

Beauzamy, B.: Introduction to Operator Theory and Invariant Subspaces. North-Holland, Amsterdam (1988)

Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li–Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373, 83–93 (2011)

Bayart, F., Matheron, E.: Dynamics of linear operators, vol. 179. Cambridge University Press, London(2009).

Costakis, G., Sambarino, M.: Topologically mixing hypercyclic operators. Proc. Am. Math. Soc. 132, 385–389 (2004)

Devaney, R.L.: An introduction to chaotic dynamical systems, 2nd edn. Addison-Wesley Studies in Nonlinearity. Addison-Wesley Publishing Company Advanced Book Program. Redwood City (1989)

Feldman, N.: Hypercyclicity and supercyclicity for invertible bilateral weighted shifts. Proc. Am. Math. Soc. 131, 479–485 (2003)

Grosse-Erdmann, K.-G.: Hypercyclic and chaotic weighted shifts. Studia Math. 139(1), 47–68 (2000)

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

Hou, B., Cui, P., Cao, Y.: Chaos for Cowen-Douglas operators. Proc. Am. Math. Soc 138, 929–936 (2010)

Hou, B., Tian, G., Shi, L.: Some dynamical properties for linear operators. Ill. J. Math. 53, 857–864 (2009)

Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Monthly 82(10), 985–992 (1975)

Martínez-Giménez, F., Oprocha, P., Peris, A.: Distributional chaos for backward shifts. J. Math. Anal. Appl. 351, 607–615 (2009)

Müller, V., Peris, A.: A Problem of Beauzamy on Irregular Operators (2011). (Preprint)

Oprocha, P.: Distributional chaos revisited. Trans. Am. Math. Soc. 361, 4901–4925 (2009)

Oprocha, P.: A quantum harmonic oscillator and strong chaos. J. Phys. A 39(47), 14559–14565 (2006)

Schweizer, B., Smítal, J.: Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Am. Math. Soc. 344(2), 737–754 (1994)

Wu, X., Zhu, P.: The principal measure of a quantum harmonic oscillator. J. Phys. A 44(505101), 6 (2011)

[-]

recommendations

 

This item appears in the following Collection(s)

Show full item record