Skip to main content
×
×
Home

Li–Yorke chaos in linear dynamics

  • N. C. BERNARDES (a1), A. BONILLA (a2), V. MÜLLER (a3) and A. PERIS (a4)
Abstract

We obtain new characterizations of Li–Yorke chaos for linear operators on Banach and Fréchet spaces. We also offer conditions under which an operator admits a dense set or linear manifold of irregular vectors. Some of our general results are applied to composition operators and adjoint multipliers on spaces of holomorphic functions.

Copyright
References
Hide All
[1]Ansari S. I.. Existence of hypercyclic operators on topological vector spaces. J. Funct. Anal. 148(2) (1997), 384390.
[2]Bartoll S., Martínez-Giménez F. and Peris A.. The specification property for backward shifts. J. Differ. Eq. Appl. 18(4) (2012), 599605.
[3]Bayart F. and Matheron É.. Dynamics of Linear Operators (Cambridge Tracts in Mathematics, 179). Cambridge University Press, Cambridge, 2009.
[4]Beauzamy B.. Introduction to Operator Theory and Invariant Subspaces. North-Holland, Amsterdam, 1988.
[5]Bermúdez T., Bonilla A., Martínez-Giménez F. and Peris A.. Li–Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373(1) (2011), 8393.
[6]Bernal-González L.. On hypercyclic operators on Banach spaces. Proc. Amer. Math. Soc. 127(4) (1999), 10031010.
[7]Bernal-González L. and Montes-Rodríguez A.. Universal functions for composition operators. Complex Variables Theory Appl. 27(1) (1995), 4756.
[8]Bernardes N. C. Jr, Bonilla A., Müller V. and Peris A.. Distributional chaos for linear operators. J. Funct. Anal. 265 (2013), 21432163.
[9]Bonet J. and Peris A.. Hypercyclic operators on non-normable Fréchet spaces. J. Funct. Anal. 159(2) (1998), 587595.
[10]Bourdon P. S.. Invariant manifolds of hypercyclic vectors. Proc. Amer. Math. Soc. 118(3) (1993), 845847.
[11]Godefroy G. and Shapiro J. H.. Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98(2) (1991), 229269.
[12]Grosse-Erdmann K.-G. and Peris Manguillot A.. Linear Chaos (Universitext). Springer, London, 2011.
[13]Herrero D. A.. Limits of hypercyclic and supercyclic operators. J. Funct. Anal. 99(1) (1991), 179190.
[14]Hou B., Tian G. and Shi L.. Some dynamical properties for linear operators. Illinois J. Math. 53(3) (2009), 857864.
[15]Hou B., Tian G. and Zhu S.. Approximation of chaotic operators. J. Operator Theory 67(2) (2012), 469493.
[16]Li T. Y. and Yorke J. A.. Period three implies chaos. Amer. Math. Monthly 82(10) (1975), 985992.
[17]Martínez-Giménez F., Oprocha P. and Peris A.. Distributional chaos for operators with full scrambled sets. Math. Z. 274 (2013), 603612.
[18]Meise R. and Vogt D.. Introduction to Functional Analysis. The Clarendon Press, Oxford University Press, New York, 1997.
[19]Piórek J.. On the generic chaos in dynamical systems. Univ. Iagel. Acta Math. 25 (1985), 293298.
[20]Prǎjiturǎ G. T.. Irregular vectors of Hilbert space operators. J. Math. Anal. Appl. 354(2) (2009), 689697.
[21]Rudin W.. Function Theory in Polydiscs. W. A. Benjamin, Inc., New York, 1969.
[22]Rudin W.. Function Theory in the Unit Ball of ℂn. Springer, Berlin, 1980.
[23]Snoha L.. Generic chaos. Comment. Math. Univ. Carolin. 31(4) (1990), 793810.
[24]Snoha L.. Dense chaos. Comment. Math. Univ. Carolin. 33(4) (1992), 747752.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 30 *
Loading metrics...

Abstract views

Total abstract views: 170 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 16th December 2017. This data will be updated every 24 hours.