具有Bogdanov-Takens型折叠点的快慢系统的周期轨道与混沌
Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points
摘要：
利用几何奇异扰动方法和blow-up方法，证明了快子系统中存在Bogdanov-Takens歧点的快慢型奇异摄动问题的稳定周期轨道和混沌不变集的存在性.特别地，Blow-up方法被有效地用于分析Bogdanov-Takens型折叠点附近的流动，以表明折叠点附近的慢流形在Blow-up空间中沿着第一Painlevé方程的Boutroux tritronquée解扩展。
英文摘要：
The existence of stable periodic orbits and chaotic invariant sets of singularly perturbed problems of fast-slow type having Bogdanov-Takens bifurcation points in its fast subsystem is proved by means of the geometric singular perturbation method and the blow-up method. In particular, the blow-up method is effectively used for analyzing the flow near the Bogdanov-Takens type fold point in order to show that a slow manifold near the fold point is extended along the Boutroux's tritronquée solution of the first Painlevé equation in the blow-up space.
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