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

In: Essays in Mathematics and its Applications

Author

Listed:
  • Alessandro Fortunati

    (University of Bristol, School of Mathematics)

  • Stephen Wiggins

    (University of Bristol, School of Mathematics)

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.

Suggested Citation

  • Alessandro Fortunati & Stephen Wiggins, 2016. "The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence," Springer Books, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Essays in Mathematics and its Applications, pages 89-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31338-2_5
    DOI: 10.1007/978-3-319-31338-2_5
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