一类两点异宿环中含马蹄的充分条件

A Sufficient Condition of a Class of Two Points Heteroclinic Loop Having Horseshoe

本文对一类含有鞍点、鞍焦点的两点异宿环的三维自治向量场,通过选取适当的局部坐标系并利用两奇点的小邻域内线性化向量场的流构造了庞加莱映射,并给出了庞加莱映射含有可数无穷多个马蹄的一个充分条件。

In this paper, for a class of three-dimensional autonomous vector field which has heteroclinic loop containing two hyperbolic fixed points, a saddle point and a saddle-focus point, we structure the Poincare map by choosing appropriate local coordinate system and using the flow of linearized vector field inside the small neighborhood of the two fixed points and present a sufficient condition of the Poincare map possessing a countable infinite horseshoes.