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

Alessandro Fortunati () and Stephen Wiggins ()
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Alessandro Fortunati: University of Bristol, School of Mathematics
Stephen Wiggins: University of Bristol, School of Mathematics

A chapter in Essays in Mathematics and its Applications, 2016, pp 89-99 from Springer

Abstract: 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.

Keywords: Normal Form; Hamiltonian System; Integrable Hamiltonian System; Homological Equation; General Time Dependence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31338-2_5

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

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