  We survey the theory of attractors of nonlinear Hamiltonian partial
differential equations since its appearance in 1990. These are results on
global attraction to stationary states, to solitons and to stationary orbits,
on adiabatic effective dynamics of solitons and their asymptotic stability.
Results of numerical simulation are given.
  The obtained results allow us to formulate a new general conjecture on
attractors of $G$ -invariant nonlinear Hamiltonian partial differential
equations.
  This conjecture suggests a novel dynamical interpretation of basic quantum
phenomena: Bohr's transitions between quantum stationary states, wave-particle
duality and probabilistic interpretation.
