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

作者：Gelfreich V^*; Gelfreikh N

来源：Regular & Chaotic Dynamics, 2010, 15(2-3): 300-318.

DOI：10.1134/S1560354710020164

• area-preserving map
• unique normal form
• parabolic fixed point

We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers +/- 1 at E > = 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.

• 出版日期2010-6