On attractors of nonlinear Hamiltonian equations

Alexander Komech Moscow State University

For generic nonlinear Hamiltonian equation, the attractor is the set of all stationary states. For generic equations with a symmetry group, the attractor is the set of all solitary waves. The problem and the results are inspired by the N.Bohr postulate on transitions to quantum stationary states and Schroedinger’s identification of the quantum stationary states to the solitary waves corresponding to the gauge symmetry group.