Ergodic Phenomena in Differential Dynamics

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One of the main problems in the Differential Dynamics is the analysis of dynamical systems with non-uniform hyperbolic behaviour. In this connection D. Kosygin and I work on the construction of standard maps without KAM-islands. Another problem which is an essential part of the proposal is to study Navier-stokes equations with random forcing and to investigate properties of their stationary distributions. One of the main problems in the theory of chaos and differential dynamics is to study dynamical systems with the mixture of regular and chaotic behaviour. One part of the proposal is devoted to the study of a big class of such systems which includes the famous standard map. I am also planning to work on various problems of mathematical and statistical hydrodynamics.