Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium

Alessandro Fortunati, Stephen R Wiggins

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

1 Citation (Scopus)
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Abstract

The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The problem can be solved either under some non-resonance hypotheses on the spectrum of the linear part or if the non-linear term is assumed to be (slowly) decaying in time. This paper "completes" a pioneering work of Pustil'nikov in which, despite under weaker non-resonance hypotheses, the nonlinearity is required to be asymptotically autonomous. The result is obtained as a consequence of the existence of a strong normal form for a suitable class of real-analytic Hamiltonians with non-autonomous perturbations.
Original languageEnglish
Article number092703
Number of pages10
JournalJournal of Mathematical Physics
Volume57
Issue number9
Early online date23 Sep 2016
DOIs
Publication statusPublished - Sep 2016

Keywords

  • Primary: 37J40
  • Secondary: 37B55
  • 37J25

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