具有Hamilton未扰动部分的二维自治系统的广义Normal Forms
Generalized Normal Forms of Two-Dimensional Autonomous Systems with a Hamiltonian Unperturbed Part
摘要：
对于具有任意次Hamilton拟齐次未扰动部分的二维自治常微分方程组，引入了广义伪Hamilton规范形（GPHNF）及其有效的构造方法.的条款，可以另外消除在GPHNF建设性的区别，它表明，删除后，GPHNF成为一个广义范式（GNF）。通过使用所介绍的方法，所有的GNF的情况下，系统的未扰动部分是Hamilton的，并有单项式的组件，这允许推广Takens，Baider和Sanders，以及Basov等人的一些结果。
英文摘要：
Generalized pseudo-Hamiltonian normal forms (GPHNF) and an effective method of obtaining them are introduced for two-dimensional systems of autonomous ODEs with a Hamiltonian quasi-homogeneous unperturbed part of an arbitrary degree. The terms that can be additionally eliminated in a GPHNF are constructively distinguished, and it is shown that after removing them GPHNF becomes a generalized normal form (GNF). By using the introduced method, all the GNFs are obtained in cases where the unperturbed part of the system is Hamiltonian and has monomial components, which allowed to generalize some results by Takens, Baider and Sanders, as well as Basov et al.
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