Mathematics

We utilize the observation made by V.V. Kozlov that the  Classical Mechanics with one degree of freedom can be connected with  some hydrodynamic type system. We generalize this observation and  moreover prove that Classical Mechanics with one degree of freedom can  be connected with hydrodynamic type systems, which are hydrodynamic  reductions of the Benney hydrodynamic chain. Thus, we describe a  family of Classical Mechanics with one degree of freedom parameterized  by 2N arbitrary functions of a single variable. This talk is based on  a small part of a common research made together with Professor Sergey  Tsarev.