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Topologically transitive skew-products of backward shift operators and hypercyclicity
Author(s):
George
Costakis;
Demetris
Hadjiloucas
Journal:
Proc. Amer. Math. Soc.
136
(2008),
937-946.
MSC (2000):
Primary 47A16, 28D99
Posted:
November 30, 2007
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Abstract:
In this article we look at skew-products of multiples of the backward shift and examine conditions under which the skew-product is topologically transitive or hypercyclic in the second coordinate. We also give an application of the theory to iterated function systems of multiples of backward shift operators.
References:
-
- 1.
- L. Arnold, Random Dynamical Systems, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. MR 1723992 (2000m:37087)
- 2.
- F. Bayart, S. Grivaux, Hypercyclicity and unimodular point spectrum, J. Funct. Anal. 226 (2005) 281-300. MR 2159459 (2006i:47014)
- 3.
- F. Bayart, S. Grivaux, Frequently hypercyclic operators, Trans. Amer. Math. Soc. 358 (2006) 5083-5117. MR 2231886 (2007e:47013)
- 4.
- L. Bernal-Gonzalez and K. -G. Grosse-Erdmann, The hypercyclicity criterion for sequences of operators, Studia Math. 157 (2003) 17-32. MR 1980114 (2003m:47013)
- 5.
- J. Bès and A. Peris, Hereditarily hypercyclic operators, J. Funct. Anal. 167 (1999) 94-112. MR 1710637 (2000f:47012)
- 6.
- J. Bonet, F. Martinez-Gimenez and A. Peris, Linear chaos on Frechet spaces, Dynamical systems and functional equations (Murcia, 2000). Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003) 1649-1655. MR 2015614 (2004i:47016)
- 7.
- R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987) 281-288. MR 884467 (88g:47060)
- 8.
- G. Godefroy and J. H. Shapiro, Operators with dense invariant cyclic manifolds, J. Funct. Anal. 98 (1991) 229-269. MR 1111569 (92d:47029)
- 9.
- S. Grivaux, Hypercyclic operators, mixing operators, and the bounded steps problem, J. Operator Theory 54 (2005) 147-168. MR 2168865 (2006k:47021)
- 10.
- K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999) no. 3, 345-381. MR 1685272 (2000c:47001)
- 11.
- K.-G. Grosse-Erdmann, Recent developments in hypercyclicity, RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. (2003) 273-286. MR 2068180 (2005c:47010)
- 12.
- A. Katok, B. Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, 1995. MR 1326374 (96c:58055)
- 13.
- C. Kitai, Invariant closed sets for linear operators, Dissertation, University of Toronto (1982).
- 14.
- F. León-Saavedra, Notes about the hypercyclicity criterion, Math. Slovaca, 53 (2003) 313-319. MR 2025025 (2004k:47010)
- 15.
- A. Montes-Rodriguez and H. N. Salas, Supercyclic subspaces, Bull. London Math. Soc. 35 (2003) 721-737. MR 2000019 (2004d:47022)
- 16.
- S. Rolewicz, On orbits of elements, Studia Math., 32 (1969) 17-22. MR 0241956 (39:3292)
- 17.
- J. H. Shapiro, Notes on the Dynamics of Linear Operators, Unpublished Lecture Notes, (available at www.math.msu.edu/ ˜shapiro).
- 18.
- P. Walters, An introduction to ergodic theory, Graduate Texts in Mathematics, Springer-Verlag, New York-Berlin, 1982. MR 648108 (84e:28017)
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Additional Information:
George
Costakis
Affiliation:
Department of Mathematics, University of Crete, Knossos Avenue, GR-714 09, Heraklion, Crete, Greece
Email:
costakis@math.uoc.gr
Demetris
Hadjiloucas
Affiliation:
The School of Computer Science and Engineering, Cyprus College, 6 Diogenes Street, Engomi, P. O. Box 22006, 1516 Nicosia, Cyprus
Email:
dhadjiloucas@cycollege.ac.cy
DOI:
10.1090/S0002-9939-07-09001-6
PII:
S 0002-9939(07)09001-6
Keywords:
Hypercyclic operators,
skew-product
Received by editor(s):
August 22, 2006
Received by editor(s) in revised form:
November 7, 2006
Posted:
November 30, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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