Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-30T23:48:02.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows

Published online by Cambridge University Press:  01 October 2007

T. KALMES
T. KALMES*
Affiliation:
Universität Trier, 54286 Trier, Germany (email: kalm4501@uni-trier.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

We characterize when C0-semigroups induced by semiflows are hypercyclic, topologically mixing, or chaotic both on spaces of integrable functions and on spaces of continuous functions. Furthermore, we give characterizations of transitivity for weighted composition operators on these spaces.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 5 , October 2007 , pp. 1599 - 1631
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Bermúdez, T., Bonilla, A., Conejero, J. A. and Peris, A.. Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Studia Math. 170 (2005), 57–75.CrossRefGoogle Scholar
[2]Bermúdez, T., Bonilla, A. and Martinón, A.. On the existence of chaotic and hypercyclic semigroups on Banach spaces. Proc. Amer. Math. Soc. 131 (2002), 2435–2441.CrossRefGoogle Scholar
[3]Conejero, J. A.. Operadores y Semigrupos de Operadores en Espacios de Fréchet y Espacios Localmente Convexos. PhD Thesis, Universidad Politécnica de Valencia, 2005.Google Scholar
[4]Deimling, K.. Nonlinear Functional Analysis. Springer, Berlin, 1985.CrossRefGoogle Scholar
[5]Desch, W., Schappacher, W. and Webb, G. F.. Hypercyclic and chaotic semigroups of linear operators. Ergod. Th. & Dynam. Sys. 17 (1997), 793–819.CrossRefGoogle Scholar
[6]Elstrodt, J.. Maß- und Integrationstheorie. Springer, Berlin, 1996.CrossRefGoogle Scholar
[7]Engel, K. J. and Nagel, R.. One-Parameter Semigroups for Linear Evolution Equations. Springer, Berlin, 2000.Google Scholar
[8]Godefroy, G. and Shapiro, J. H.. Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98 (1991), 229–269.CrossRefGoogle Scholar
[9]Grosse-Erdmann, K. G.. Universal families and hypercyclic operators. Bull. Amer. Math. Soc. 36(3) (1999), 345–381.CrossRefGoogle Scholar
[10]Grosse-Erdmann, K. G.. Recent developments in hypercyclicity. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97(2) (2003), 273–286.Google Scholar
[11]Grosse-Erdmann, K. G.. Hypercyclic and chaotic weighted shifts. Studia Math. 139 (2000), 47–68.CrossRefGoogle Scholar
[12]Matsui, M., Yamada, M. and Takeo, F.. Supercyclic and chaotic translation semigroups. Proc. Amer. Math. Soc. 131 (2003), 3535–3546.Google Scholar
[13]Matsui, M., Yamada, M. and Takeo, F.. Erratum to ‘Supercyclic and chaotic translation semigroups’. Proc. Amer. Math. Soc. 132 (2004), 3751–3752.CrossRefGoogle Scholar
[14]Matsui, M. and Takeo, F.. Chaotic semigroups generated by certain differential operators of order 1. SUT J. Math. 37 (2001), 51–67.CrossRefGoogle Scholar
[15]Myjak, J. and Rudnicki, R.. Stability versus chaos for a partial differential equation. Chaos Solitons Fractals 14 (2002), 607–612.CrossRefGoogle Scholar
[16]Rolewicz, S.. On orbits of elements. Studia Math. 32 (1969), 17–22.CrossRefGoogle Scholar
[17]Rudin, W.. Real and Complex Analysis. McGraw-Hill, New York, 1987.Google Scholar
[18]Salas, H.. Hypercyclic weighted shifts. Trans. Amer. Math. Soc. 347 (1995), 993–1004.CrossRefGoogle Scholar
[19]Singh, R. K. and Manhas, J. S.. Composition Operators on Function Spaces. North-Holland, Amsterdam, 1993.Google Scholar