 0616 Andrea Carati
 An averaging theorem for Hamiltonian dynamical systems in the thermodynamic limit
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Jan 20, 06

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Abstract. It is shown how to perform some steps of perturbation theory if one
assumes a measuretheoretic point of view, i.e. if one renounces to
control the evolution of the single trajectories, and the attention is
restricted to controlling the evolution of the measure of some
meaningful subsets of phasespace. For a system of coupled rotators,
estimates uniform in $N$ for finite specific energy can be obtained in
quite a direct way . This is achieved by making reference not to the
sup norm, but rather, following Koopman and von Neumann, to the much
weaker $L^2$ norm.
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