Lie-point symmetries and nonlinear dynamical systems

  • Authors:

  • G. Cicogna;G. Gaeta

  • Affiliations:

  • Dipartimento di Fisica, Università di Pisa Piazza Torricelli 2, 56126 Pisa, Italy;Department of Mathematics, Loughborough University Loughborough LE11 3TU, England

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1997

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Abstract

Nonlinear symmetries of finite dimensional dynamical systems are related to nonlinear normal forms and center manifolds in the neighbourhood of a singular point. Certain abstract results can be used algorithmically to construct the normal forms and/or the center manifold up to a given order in the perturbation expansion. We also argue that for this task, approximate symmetries are as useful as exact ones.