Hartman-Grobman theorems along hyperbolic stationary trajectories

Discrete and Continuous Dynamical Systems

Volumn 17, Issue 2, 2007, Pages 281-292

  Coayla Teran, Edson A ^a   Mohammed, Salah Eldin A ^b   Ruffino, Paulo Régis C ^c  

^a FEDERAL UNIVERSITY OF BAHIA   (Brazil)

^b Southern Illinois University at Carbondale   (United States)

^c UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Hartman Grobman theorems; Hyperbolic stationary trajectories; Random dynamical systems

Indexed keywords

EID: 33847740370     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (19)

1. ARNOLD, L., "Random Dynamical Systems," Springer, Berlin (1998).
2. ARNOLD, L. and M. SCHEUTZOW, Perfect cocycles through stochastic differential equations. Prob. Th. Rel. Fields, 101, p. 65-88, 1995.
3. ARNOLD, L. AND P. IMKELLER, Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory, Stochastic Processes and their Applications, 62, 19-54, 1996.
4. BAXENDALE, P., Asymptotic behavior of stochastic flow of diffeomorphism, in "Stochastic Processes and their Applications" (Ed. K. Itô and T. Hida.), - Proceedings of the International Conference in Nagoya, July 2-6, 1985. Lecture Notes Math. 1203. Springer, 1986.
5. BOXLER, P., A Stochastic version of center manifold theory, Probability Theory and Related Fields.83, (1989), 509-545.
6. CARVERHILL, A., Flows of stochastic dynamical systems, Ergodic theory, Stochastics, 14 (1985), 273-317.
7. COAYLA-TERAN, E.A. AND P.R.C. RUFFINO, Stochastic versions of Hartman-Grobman theorems, Stochastics and Dynamics, 4(4)(2004), 571-593.
8. CONG, N. D., Topological classification of linear hyperbolic cocycles, Journal of Dynamics and Differential Equations, 8, no. 3 (1996), 427-467.
9. GROBMAN, D. M., Homeomorphisms of systems of differential equations, Dokl. Akad. Nauk SSSR, 128 (1959), 880-881.
10. HARTMAN, P., A lemma in the theory of structural stability of differential equations, Proc. A.M.S. 11 (1960), 610-620.
11. HARTMAN, P., On local homeomorphisms of Euclidean spaces, Bol. Soc. Math. Mexicana, 5 (1960), 220-241.
12. KATOK, A. AND B. HASSELBLATT, "Introduction to the Modern Theory of Dynamical Systems," CUP, 1999.
13. MOHAMMED, S.-E. A. AND M. SCHEUTZOW, The stable manifold theorem for stochastic differential equations, Annals of Prob., Vol. 27(1999), pp. 615-652.
14. PALIS JR., J. AND W. DE MELO, "Geometric theory of Dynamical Systems: an Introduction," Springer-Verlag, New York, Heidelberg, Berlin, 1982.
15. RUELLE, D., Ergodic theory of differentiable dynamical systems, Publ. IHES 50 (1979) 275-305.
16. RUFFINO, P. R. C., Rotation number for stochastic dynamical systems, Stoch. and Stoch. Reports, 60 (1997), pp. 289-318.
17. SPARROW, C., "The Lorentz Equations: Bifurcations, Chaos and Strange Attractors," Springer-Verlag, New York, 1982.
18. STERNBERG, S., Local contractions and a theorem of Poincaré, Amer. J. Math. vol. 79 (1957), 809-824.
19. WANNER, T., Linearization of random dynamical systems, in "Dynamics Reported" (Eds.John, C., Kirchgraaber, U., and Walter H. O.), Vol. 4, Springer, Berlin, Heidelberg, New York (1994).