The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds

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• 作者：Huagui Duan ; Yiming Long ; Wei Wang
• 关键词：Mathematics Subject Classification53C22 ; 58E05 ; 58E10
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：55
• 期：6
• 全文大小：789 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835
• 卷排序：55

文摘

In this paper, we first generalize the common index jump theorem for symplectic matrix paths proved in Long and Zhu (Ann Math 155:317–368, 2002), and get an enhanced version of it. Then we give several applications providing lower bounds on the number of distinct closed geodesics in various settings on compact simply-connected Finsler manifolds.