 05235 Paolo Perfetti
 A Nekhoroshev theorem for some
infinitedimensional systems
(439K, ps)
Jul 1, 05

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Abstract. We study the persistence for
long times of the solutions of some infinitedimensional discrete
hamiltonian systems with {\it formal hamiltonian}
$\sum_{i=1}^\infty h(A_i) + V(\vp),$ $(A,\vp)\in {\Bbb R}^{\Bbb
N}\times {\Bbb T}^{\Bbb N}.$ $V(\vp)$ is not needed small and the
problem is perturbative being the kinetic energy unbounded. All
the initial data $(A_i(0), \vp_i(0)),$ $i\in {\Bbb N}$ in the
phasespace ${\Bbb R}^{\Bbb N} \times {\Bbb T}^{\Bbb N},$ give
rise to solutions with $\mod A_i(t)  A_i(0).$ close to zero for
exponentiallylong times provided that $A_i(0)$ is large enough
for $\mod i.$ large. We need $\o \partial h,\partial
A_i,{\scriptstyle (A_i(0))}$ unbounded for $i\to+\infty$ making
$\vp_i$ a {\it fast variable}; the greater is $i,$ the faster is
the angle $\vp_i$ (avoiding the resonances). The estimates are
obtained in the spirit of the averaging theory reminding the
analytic part of Nekhoroshevtheorem.
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