Invariant measures for some partial differential equations

We construct invariant measures for Hamiltonian systems such as the nonlinear Schrrdinger equation or the wave equation in order to prove Poisson’s recurrence. The particular case of schemes (finite dimensional spaces) is also treated in order to explain the recurrence phenomenon which is observed during numerical simulations.

2

Physica D, Nonlinear Phenomena, 82(4), 340–364 (1995)