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arXiv · 0912.2922

Unique normal forms for area preserving maps near a fixed point with neutral multipliers

V. Gelfreich·N. Gelfreikh
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Abstract

We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers -1 or +1 at epsilon=0. Our study covers both the orientation-preserving and orientation-reversing cases. In these cases Birkhoff normal forms do not provide a substantial simplification of the system. In the paper we prove that the Takens normal form vector field can be substantially simplified. We also show that if certain non-degeneracy conditions are satisfied no further simplification is generically possible since the constructed normal forms are unique. In particular, we provide a full system of formal invariants with respect to formal coordinate changes.

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V. Gelfreich, N. Gelfreikh. 2009-12-15. Unique normal forms for area preserving maps near a fixed point with neutral multipliers. https://doi.org/10.1134/s1560354710020164

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