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arXiv · 0809.1614

Unique resonant normal forms for area preserving maps at an elliptic fixed point

V. Gelfreich·N. Gelfreikh
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Abstract

We construct a resonant normal form for an area-preserving map near a generic resonant elliptic fixed point. The normal form is obtained by a simplification of a formal interpolating Hamiltonian. The resonant normal form is unique and therefore provides the formal local classification for area-preserving maps with the elliptic fixed point. The total number of formal invariants is infinite. We consider the cases of weak (of order $n\ge5$) and strong (of order $n=3,4$) resonances. We also construct unique normal forms for analytic families of area-preserving maps. We note that our constructions involve non-linear grading functions.

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V. Gelfreich, N. Gelfreikh. 2008-09-09. Unique resonant normal forms for area preserving maps at an elliptic fixed point. https://doi.org/10.1088/0951-7715%2F22%2F4%2F006

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