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

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 terms. 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 Pustyl’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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Sep 01, 2016
Source ID
10.1063/1.4962802

Entities

People

  • Alessandro Fortunati
  • Stephen Wiggins

Organizations

  • Office of Naval Research
  • University of Bristol

Tags

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Autonomy