Shadowing property. Probabilistic aspects.

Shadowing theory study properties of approximate trajectories: sequences of points, where next one is close to image of the previous one. Such sequnces naturally appears, for example, in the presence of noise or as a result of numerical simulation.

We introduce notions of shadowing, hyperbolicity and structural stablity and briefly discuss relation between them.

In the talk we concentrate on random finite length pseudotrajectories (and trajectories). where main questions will have probabilistic nature. We formulate several questions and conjectires. We consider model ``skew-product'' example which can be reduced to a 1-dimensional random walk. This simple example, however allows us to disprove one the long-posed conjecture