We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in , in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.
Coayla-Teran, Edson A., Mohammed, Salah-Eldin A. and Ruffino, Paulo Régis C. "Hartman-Grobman Theorems along Hyperbolic Stationary Trajectories." (Feb 2007).