On the problem of stability for near to integrable Hamiltonian systems
The author observes some progress in Nekhoroshev's exponential stability theory made during the last decade, in particular, in the following points. (a) The actual estimates for critical values of small parameters \(\varepsilon\) in singular perturbed Hamiltonian systems for real physical problems; this is illustrated by the stability of Lagrangian point in three bodies problem for Sun-Jupiter case. (b) The extension of the concept of exponential stability with very large number of degrees of freedom and possibly to infinite systems; here a certain one-dimensional model of the gas is under consideration and the author discusses how far the suggestions of Boltzmann and Jeans may be dynamically justified. (c) Some relations between KAM and Nekhoroshev's theories; in particular, a certain stability result is obtained, called superexponential stability.
scientific article; zbMATH DE number 1184354