Systematic derivation of amplitude equations and normal forms for dynamical systems.

@article{Ipsen1998SystematicDO,
  title={Systematic derivation of amplitude equations and normal forms for dynamical systems.},
  author={Mads Ipsen and Finn Hynne and Peggy J G Sorensen},
  journal={Chaos},
  year={1998},
  volume={8 4},
  pages={834-852}
}
We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from amplitudes to physical space. At any order, the relation provides explicit expressions for all the nonvanishing coefficients of the amplitude… CONTINUE READING

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