Phase topology of one system with separated variables and singularities of the symplectic structure

Abstract

We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of variables to calculate the exact topological invariant of non-degenerate singularities and singularities appearing due to the symplectic structure degeneration. New types of non-orientable 3-atoms are found.

Corrected according to the version accepted in J. of Geometry and Physics, On-line July 2014, LaTex, 23 pp., 17 figures, 6 tables

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