Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations

Alessandro Fortunati*, Stephen Wiggins

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
299 Downloads (Pure)

Abstract

The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous integrable part, the system can be cast in an exact normal form, regardless of the properties of the frequency vector. The general case is treated by a suitable adaptation of the finite order normalization techniques usually used for Nekhoroshev arguments. The key point is that the so called “geometric part” is not necessary in this case. As a consequence, no hypotheses on the integrable part are required, apart from analyticity. The work, based on two different perturbative approaches developed by Giorgilli et al., is a generalisation of the techniques used by the same authors to treat more specific aperiodically time-dependent problems.

Original languageEnglish
Pages (from-to)247–262
Number of pages16
JournalCelestial Mechanics and Dynamical Astronomy
Volume125
Issue number2
Early online date1 Apr 2016
DOIs
Publication statusPublished - Jun 2016

Keywords

  • Aperiodic time dependence
  • Birkhoff normal forms
  • Non-autonomous Hamiltonian systems
  • Stability

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