Panayotis Panayotaros
Nekhoroshev stability of non-linear normal modes 
near an elliptic fixed point of a Hamiltonian system with symmetry 
(85K, TeX)

ABSTRACT.  We consider  
Hamiltonian systems of resonantly coupled harmonic oscillators
with a physically motivated $U(1)$ symmetry, and identify 
a class of small amplitude 
periodic orbits (the non-linear normal modes) of approximating 
systems. We show that under some additional conditions on the
quartic part of the Birkhoff normal form Hamiltonian
that are in many cases weaker than integrability and convexity,
the non-linear normal modes are Nekhoroshev stable.