Further Reductions of Normal Forms for Dynamical Systems

  title={Further Reductions of Normal Forms for Dynamical Systems},
  author={Guoting Chen and Jean Della Dora},
  journal={Journal of Differential Equations},
  • Guoting Chen, J. Dora
  • Published 1 September 2000
  • Mathematics, Computer Science
  • Journal of Differential Equations
Abstract We propose in this paper a method for obtaining a significant refinement of normal forms for dynamical systems or vector fields, with concrete and interesting applications. We use lower order nonlinear terms in the normal form for the simplifications of higher order terms. Our approach is applicable for both the non nilpotent and the nilpotent cases. For dynamical systems of dimensions 2 and 3 we give an algorithm that leads to interesting finite order normal forms which are optimal… 

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