ABSTRACT
This chapter addresses limiting processes for abstract dispersive dynamical processes on a Fréchet convergence space and the generalized Lyapunov direct method proposed by Ball. It introduces the definition of a nonsingular abstract dynamical process on a Fréchet convergence space, and demonstrates that under fairly general conditions to every such abstract dynamical process there corresponds an abstract autonomous dynamical process on an appropriate phase space. The chapter presents the generalized Lyapunov direct method for a non-autonomous D+ process on a Fréchet convergence space, i.e. the method of localization of the limiting set of motion of a D+ process using Ball-type L functionals.
