The Kolmogorov-Arnold-Moser (KAM) theorem and the Nekhoroshev theorem are the two “pillars” of canonical perturbation theory for near-integrable Hamiltonian systems. Over the years there have been many extensions and generalizations of these fundamental results, but it is only very recently that extensions of these theorems near-integrable Hamiltonian systems having explicit, and aperiodic, time dependence have been developed. We will discuss these results, with particular emphasis on the new mathematical issues that arise when treating aperiodic time dependence.
|Title of host publication||Essays in Mathematics and its Applications|
|Subtitle of host publication||In Honor of Vladimir Arnold|
|Editors||Themistocles M. Rassias, Panos M. Pardalos|
|Place of Publication||Cham|
|Publisher||Springer International Publishing AG|
|Number of pages||11|
|Publication status||Published - 15 Jun 2016|