The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence

Alessandro Fortunati, Stephen Wiggins

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

1 Citation (Scopus)

Abstract

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.
Original languageEnglish
Title of host publicationEssays in Mathematics and its Applications
Subtitle of host publicationIn Honor of Vladimir Arnold
EditorsThemistocles M. Rassias, Panos M. Pardalos
Place of PublicationCham
PublisherSpringer International Publishing AG
Pages89-99
Number of pages11
Volume9783319313368
ISBN (Electronic)9783319313382
DOIs
Publication statusPublished - 15 Jun 2016

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