Liouville平面上的动力系统及相关的严格接触系统
Dynamical systems on the Liouville plane and the related strictly contact systems
摘要：
研究了平面上保刘维尔型的向量场。我们提出了它们的局部模型，直到自然等价关系，并描述了低余维的局部分支。为了实现这一点，根据比接触等价更严格的关系，给出了一元函数的分类。此外，我们还讨论了它们与三维严格切触向量场的关系。对非同态也给出了类似的结果。
英文摘要：
We study vector fields of the plane preserving the form of Liouville. We present their local models up to the natural equivalence relation, and describe local bifurcations of low codimension. To achieve that, a classification of univariate functions is given, according to a relation stricter than contact equivalence. We discuss, in addition, their relation with strictly contact vector fields in dimension three. Analogous results for diffeomorphisms are also given.
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