Dissipative Systems: Relative Roughness, Nonroughness of Various Degrees, and Integrability

This paper is devoted to the study of relative structural stability (the roughness) dynamical systems considered not on whole space systems, but only a certain subspace it. Moreover, deformations also does coincide with admissible deformations. In particular, we consider dissipative differential equations that arise in rigid-body dynamics and theory oscillations; dissipation such may by positive or negative. We examine roughness and, under conditions, their nonroughness various degrees. discuss problems integrability these finite combinations elementary functions.