A generalization of desch-schappacher-webb criteria for chaos

Discrete and Continuous Dynamical Systems

Volumn 12, Issue 5, 2005, Pages 959-972

  Banasiak, Jacek ^a   Moszyński, Margin ^b  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

Birth and death systems; Hypercyclic operators; Infinite dimensional linear systems; Topological chaos

Indexed keywords

EID: 18144399275     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.12.959     Document Type: Article

References (18)

1. J. Banasiak and M. Lachowicz, Chaotic linear dynamical systems with applications, in: C. Kubrusly, N. Levan, M. da Silveira (Eds), Semigroups of Operators: Theory and Applications, end International Conference, Rio de Janeiro, 2001, Optimization Software Inc., Publications, New York - Los Angeles, 2002, 32-44.
2. J. Banasiak and M. Lachowicz, Chaos for a class of linear kinetic models, Compt. Rend. Acad. Sci. Paris, 329, Série IIb, 2001, 439-444.
3. J. Banasiak and M. Lachowicz, Topological chaos for birth-and-death-type models with proliferation, Math. Models Methods Appl. Sci., 12 No. 6, 2002, 755-775.
4. J. Banasiak, M. Lachowicz and M. Moszyński, Topological chaos: when topology meets medicine, Appl. Math. Letters, 16, 2003, 303-308.
5. J. Banasiak, M. Lachowicz and M. Moszyński, Chaotic behavior of semigroups related to the process of gene amplification-deamplification with cells' proliferation, submitted.
6. J. Banks, J. Brooks, G. Cairns, G. Davis and P. Stacey, On Devaney's definition of chaos, Amer. Math. Monthly, 99, 1992, 332-334.
7. R. deLaubenfels, H. Emamirad, Chaos for functions of discrete and continuous weighted shift operators, Ergod. Th. & Dynam. Systems, 21, 2001, 1411-1427.
8. W. Desch, W. Schappacher and G.F. Webb, Hypercydic and chaotic semigroups. of linear operators, Ergodic Theory Dynam. Systems, 17, 1997, 793-819.
9. R.L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd edn., Addison-Wesley, New York, 1989.
10. J. Duan, X.-C. Pu, P.-D. Liu, A. Manning, A linear chaotic quantum harmonic oscillator Appl. Math. Lett. 12 no.1, 1999, 15-19.
11. X.-C. Fu, J. Duan, Infinite-dimensional linear dynamical systems with chaoticity, J. Nonlinear Sci. 9 no.2, 1999, 197-211.
12. S. Galatolo, Global and local complexity in weakly chaotic dynamical systems, Discrete Contin. Dyn. Syst. 9 no.6, 2003, 1607-1624.
13. G. Godefroy and J.H. Shapiro, Operators with dense, invariant, cydic manifolds, J. Funct. Anal., 98, (1991), 229-269.
14. D. A. Herrero, Hypercyclic operators and chaos, J. Operator Theory, 28 (1992), 93-103.
15. T. Kato, Perturbation theory for linear operators, Springer-Verlag New York, Inc., New York 1966.
16. A. Pazy, Semigroups of linear operators and applications to PDE, Springer 1983.
17. V. Protopopescu and Y.Y. Azmy, Topological chaos for a class of linear models, Math. Models Methods Appl. Sci, 2, 1, 1992, 79-90.
18. W. Rudin, Functional Analysis, McGraw-Hill, 1973.