Bifurcation analysis of the multiple flips homoclinic orbit

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• 作者：Tiansi Zhang (1)
  Deming Zhu (2)
  
• 关键词：Orbit flip ; Inclination flips ; Homoclinic orbit ; Resonance ; 37C29 ; 34C23 ; 34C37
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：36
• 期：1
• 页码：91-104
• 全文大小：320 KB
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• 作者单位：Tiansi Zhang (1)
  Deming Zhu (2)
  
  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
  2. Department of Mathematics, East China Normal University, Shanghai, 200062, China
  
• ISSN：1860-6261

文摘

A high-codimension homoclinic bifurcation is considered with one orbit flip and two inclination flips accompanied by resonant principal eigenvalues. A local active coordinate system in a small neighborhood of homoclinic orbit is introduced. By analysis of the bifurcation equation, the authors obtain the conditions when the original flip homoclinic orbit is kept or broken. The existence and the existence regions of several double periodic orbits and one triple periodic orbit bifurcations are proved. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately.