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

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

2008-09-09

arxiv.org/abs/0809.1614v1

Mathematics

Dynamical Systems

37 pages, 5 figures

Scientific paper

10.1088/0951-7715/22/4/006

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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