98-271 Avanzini F., Bambusi D.

Stability properties in Hamiltonian perturbations of resonant PDE's with symmetry: the case of NLS (446K, PS) Apr 14, 98

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Abstract. In this paper we present some stability results for Hamiltonian PDE's which have an exact symmetry, and are perturbations of a linear resonant system. We also give an application to some nonlinear Schr\"odinger equations constructing infinitely many families of elliptic periodic orbits, one of which is orbitally stable, and infinitely many families of ``approximatively invariant'' 2-dimensional tori, which are stable over very long times.

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