TOTALLY DISSIPATIVE DYNAMICAL PROCESSES AND THEIR UNIFORM GLOBAL ATTRACTORS

摘要

We discuss the existence of the global attractor for a family of processes U-sigma(t, tau) acting on a metric space X and depending on a symbol sigma belonging to some other metric space Sigma. Such an attractor is uniform with respect to sigma is an element of Sigma, as well as with respect to the choice of the initial time tau is an element of R. The existence of the attractor is established for totally dissipative processes without any continuity assumption. When the process satisfies some additional (but rather mild) continuity-like hypotheses, a characterization of the attractor is given.