Abstract
The problem of the existence of normal forms for symplectic maps inR 2n is analyzed using a technique based on the generating functions. We discuss extensively the case of a map with an elliptic fixed point: both the resonant and non resonant cases are presented.
Explicit algorithms to calculate the analytic expansions of the normal forms and the associated canonical transformation are also provided.
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Bazzani, A. Normal forms for symplectic maps of R2n . Celestial Mechanics 42, 107–128 (1987). https://doi.org/10.1007/BF01232951
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DOI: https://doi.org/10.1007/BF01232951