Lecture Notes On Dissipative Bose-Einstein Equations

This book develops the theory of global attractors for a class of Schrödinger type equations in presence of a quadratic potential. Two examples are treated in details, a rigorous treatement of existence and uniqueness of solutions for the nonlinear evolution equations that generate the infinite dimensional dynamical systems of the title. Attention then turns to the global attractor, a finite dimensional subset of the infinite dimensinal phase space that determinates the asymptotic dynamics. In particular, the concluding Chapter investigate in what sense the dynamics restricted to the attractors are themselves "finite dimensional".