Sessions Of The Workshop Of The Mathematics And Mechanics Department Of Lomonosov Moscow State University, 'urgent Problems Of Geometry And Mechanics' Named After V. V. Trofimov

摘要

Problems arising in many varied fields of natural sciences, especially those at the interface of geometry and mechanics, foster the development of a new qualitative analytical apparatus of study. Thus, for example, a qualitative theory of dissipative systems having applications in many fields of natural sciences has appeared. In many problems the main emphasis is on the topological classification of types of trajectories and regions of their location in the phase space of dynamical systems under study. The qualitative study of systems with continuous time (flows) on smooth manifolds requires new methods to be developed. For example, statements obtained for purely dissipative systems and for systems with the so-called variable dissipation (this is a name for systems having dissipation of both signs) came as a continuation of the Poincare-Bendixon theory for flows on closed two-dimensional manifolds and the topological classification of flows.