Nekhoroshev theorem nearly integrable systems

Theorem[Nekhoroshev]. Consider nearly integrable systems with n degrees of freedom ... 

The perturbation strength for which the Nekhoroshev s theorem holds is also so small that it cannot be applied to realistic physical and chemical situations. Indeed it was shown that the range of perturbation strength is much smaller than the situation where the power spectrum density of observables exhibits a continuous one [24]. This means that, in its rigorous sense, the Nekhoroshev s theorem can only be applied to sufficiently weak perturbed systems. For the same reason as mentioned above, Nekhoroshev s theorem is nevertheless a key guiding principle to sticky or stagnant motions in nearly integrable Hamiltonian systems. 

Benettin, G., Galgani, L., Giorgilli, A. (1985). A proof of Nekhoroshev s theorem for the stability times in nearly integrable Hamiltonian systems. Cel. Mech., 37 1-25. Benettin, G., Gallavotti, G. (1986). Stability of motions near resonances in quasi-integrable Hamiltonian systems. Joum. Stat. Phys., 44 293-338. 

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