Bambusi D.
 Averaging Theorem for Quasilinear Hamiltonian PDEs 
in Arbitrary Space Dimensions
(82K, TeX)

ABSTRACT.  We study the dynamics of  quasilinear Hamiltonian wave
equations with Dirichlet boundary conditions in an $n$--dimensional
parallepided. We prove
an averaging theorem according to which the solution corresponding to
an arbitrary small amplitude smooth initial datum remains arbitrarily
close to a finite dimensional torus up to very long times. We expect
the result to be valid for a very general class of quasilinear
Hamiltonian equations.