华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (5): 13-23.

• 数学 统计学 • 上一篇    下一篇

反转系统中异宿环附近的同宿轨和周期轨(英)

孙莹, 朱德明   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2005-04-03 修回日期:2005-10-21 出版日期:2006-09-25 发布日期:2012-11-27

Reversible Homoclinic and Periodic Orbits Near Heteroclinic Loop

SUN Ying, ZHU De-ming   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2005-04-03 Revised:2005-10-21 Online:2006-09-25 Published:2012-11-27

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.

关键词: 同宿轨, 异宿轨, 反转性, 鞍焦点 ,  ,

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.

Key words: homoclinic orbits, heteroclinic orbits, reversibility, saddle-focus  

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