Unique normal forms for area preserving maps near a fixed point with neutral multipliers
Unique normal forms for area preserving maps near a fixed point with neutral multipliers
复制标题
具有中性乘数的固定点附近区域保留地图的独特范式
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
N. Gelfreikh
中科院分区：
文献类型：
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作者：
V. Gelfreich;N. Gelfreikh
我们研究了具有中性乘子±1的不动点的保面积映射族的正规形式。我们的研究涵盖了取向保持和取向逆转两种情况。在这些情况下，伯克霍夫范式不能提供系统的实质性简化。本文证明了Takens范式向量场可以被大大简化。我们还证明了如果满足某些非退化条件，由于构造的范式是唯一的，因此进一步的简化一般是不可能的。特别地，我们提供了一个关于形式坐标变化的形式不变量的完整系统。
We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers ±1 at ɛ = 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.