  We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian
oscillator chains approaching their statistical asympotic states. In systems
constrained by more than one conserved quantity, the partitioning of the
conserved quantities leads naturally to localized and coherent structures. If
the phase space is compact, the final equilibrium state is governed by entropy
maximization and the final coherent structures are stable lumps. In systems
where the phase space is not compact, the coherent structures can be collapses
represented in phase space by a heteroclinic connection to infinity.
