Convergence versus integrability in Poincare-Dulac normal form
Convergence versus integrability in Poincare-Dulac normal form
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DOI：
10.4310/mrl.2002.v9.n2.a8
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发表时间：
2001-05
影响因子：
1
通讯作者：
N. Zung
中科院分区：
文献类型：
--
作者：
N. Zung
证明了求向量场的Poincare-Dulac正规化与求并线性化保持向量场的环面作用是相同的。利用这个环刻画和其他几何证明，我们证明了在非哈密顿意义下可积的局部解析向量场允许局部收敛的Poincare-Dulac正规化。这些结果将我们以前的主要结果从哈密顿情形推广到非哈密顿情形。对于等厚线矢量场的情况也给出了类似的结果。
We show that, to find a Poincare-Dulac normalization for a vector field is the same as to find and linearize a torus action which preserves the vector field. Using this toric characterization and other geometrical arguments, we prove that any local analytic vector field which is integrable in the non-Hamiltonian sense admits a local convergent Poincare-Dulac normalization. These results generalize the main results of our previous paper from the Hamiltonian case to the non-Hamiltonian case. Similar results are presented for the case of isochore vector fields.