Qualitative investigation of Hamiltonian systems by application of skew-symmetric differential forms

Abstract

A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in addition to skew-symmetric exterior differential forms, skew-symmetric differential forms, which differ in their properties from exterior forms, are used. These are skew-symmetric differential forms defined on manifolds that are nondifferentiable ones. Such manifolds result, for example, under describing physical processes by differential equations. This approach to investigation of Hamiltonian systems enables one to understand a connection between Hamiltonian systems and partial differential equations, which describe physical processes, and to see peculiarities of Hamiltonian systems and relevant phase spaces connected with this fact.