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

Alessandro Fortunati; Stephen Wiggins

doi:10.1007/978-3-319-31338-2_5

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

Alessandro Fortunati, Stephen Wiggins

Research output: Chapter in Book/Report/Conference proceeding › Chapter 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 language	English
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
Pages	89-99
Number of pages	11
Volume	9783319313368
ISBN (Electronic)	9783319313382
DOIs	https://doi.org/10.1007/978-3-319-31338-2_5
Publication status	Published - 15 Jun 2016

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10.1007/978-3-319-31338-2_5

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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.",

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The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence. / Fortunati, Alessandro; Wiggins, Stephen.

Essays in Mathematics and its Applications: In Honor of Vladimir Arnold. ed. / Themistocles M. Rassias; Panos M. Pardalos. Vol. 9783319313368 Cham : Springer International Publishing AG, 2016. p. 89-99.

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

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AU - Wiggins, Stephen

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Y1 - 2016/6/15

N2 - 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.

AB - 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.

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DO - 10.1007/978-3-319-31338-2_5

M3 - Chapter in a book

VL - 9783319313368

SP - 89

EP - 99

BT - Essays in Mathematics and its Applications

A2 - Rassias, Themistocles M.

A2 - Pardalos, Panos M.

PB - Springer International Publishing AG

CY - Cham

ER -

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

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