Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Hartman-Grobman theorems along hyperbolic stationary trajectories

Pages: 281 - 292, Volume 17, Issue 2, February 2007      doi:10.3934/dcds.2007.17.281

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Edson A. Coayla-Teran - Instituto de Matemática-UFBA, Av. Ademar de Barros s/n, 40170-110 Salvador-BA, Brazil (email)
Salah-Eldin A. Mohammed - Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, Illinois 62901, United States (email)
Paulo Régis C. Ruffino - Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 - Campinas - SP, Brazil (email)

Abstract: We extend the Hartman-Grobman theorems for discrete random dynamical systems (RDS), proved in [7], in two directions: for continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between travelling neighborhoods of trajectories and neighborhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.

Keywords:  Random dynamical systems, Hartman-Grobman theorems, hyperbolic stationary trajectories.
Mathematics Subject Classification:  Primary: 93E99, 37D40, 34A34; Secondary: 37H15.

Received: December 2005;      Revised: September 2006;      Available Online: November 2006.