Nonlinear oscillation regimes in some physical problems

Abstract

Complex nonlinear oscillation regimes having stochastic properties and allowing, detailed research of their dynamics due to presence of their separatrix approximation have been found of late in a number of problems in general theory of relativity, gas dynamics, theory of perturbations of completely integrable systems and theory of finite-dimensional approximations of hydrodynamics equations (so called systems of hydrodynamic type) [1–5]. Formulation of some of these problems is put in Sections 1, 2, 3 of the present paper, Section 4 presents the unified derivation of oscillation regimes, contained in them and the conditions sufficient for the existance of such regimes in dynamical systems of more general type. The properties of the given oscillatory regimes for concrete problems discussed in Sections 1, 2, 3 are enumerated in Section 5.