Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian.
A Hamiltonian system differing from an integrable system by a small perturbation equals, similar varepsilon is analyzed. According to the Nekhoroshev theorem, the changes in the perturbed motion of the "action" variables of the unperturbed system are small over a time interval which increases exponentially in length as varepsilon decreases linearly. If the unperturbed Hamiltonian is a quasiconvex function of these "actions," the changes in them remain small ( equals, similar varepsilon (1/2n)) over a time interval on the order of exp(const/ varepsilon (1/2n)), where n is the number of degrees of freedom of the system.
Lochak
P.
P
Ecole Normale Superieure, F-75230, Paris, FranceSpace Research Institute, Moscow, 117810, Russia.
Neishtadt
A. I.
AI