Linearization of continuous-time random dynamical systems

This talk is devoted to the linearization of continuous-time random dynamical systems.  Mathematical models of real-life problems often lead to nonlinear differential or difference equations. In general, they cannot be solved explicitly and even a qualitative analysis might be difficult. At the same time we have a well-studied and quite complete theory of linear systems. This leads to the reasonable question, under which conditions we can use linear theory for studying the nonlinear problems.

First part of the talk is devoted to the sufficient conditions of strong topological equivalence of continuous-time random dynamical system to its linearization. After, the possibility of diferentiability of the conjugating map between this systems will be discussed.