Reversible Homoclinic and Periodic Orbits Near Heteroclinic Loop
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摘要: 讨论了四维反转系统中异宿环附近的动态性质,其中的异宿轨是连接鞍焦点和鞍点的. 证明在通有条件下,该异宿环附近存在可数无穷多条1-同宿轨, 和可数无穷多个1-周期轨的单参数族,同时对这些周期轨和同宿轨作了直观描述.Abstract: This paper studied the dynamical behavior of a 4-dimensional reversible system near a heteroclinic loop connecting a saddle-focus equilibrium and a saddle one. An existence theorem concerning denumerable 1-homoclinic orbits and countable families of 1-periodic orbits was given under a generic condition; and an intuitionistic description about those orbits was also given.
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Key words:
- homoclinic orbits /
- heteroclinic orbits /
- reversibility /
- saddle-focus
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