The Fadell-Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler

详细信息    查看全文

• 作者：Hui Liu¹ ; ^{huiliu@ustc.edu.cn}
• 关键词：53C22 ; 58E05 ; 58E10
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2540-2553
• 全文大小：298 K
• 卷排序：262

文摘

In this paper, we prove that for every irreversible Finsler n  -dimensional real projective space (RPn,F)(RPn,F) with reversibility λ and flag curvature K   satisfying 169(λ1+λ)2<K≤1 with λ<3λ<3, there exist at least n−1n−1 non-contractible closed geodesics. In addition, if the metric F   is bumpy with 6425(λ1+λ)2<K≤1 and λ<53, then there exist at least 2[n+12] non-contractible closed geodesics, which is the optimal lower bound due to Katok's example. The main ingredients of the proofs are the Fadell–Rabinowitz index theory of non-contractible closed geodesics on (RPn,F)(RPn,F) and the S1S1-equivariant Poincaré series of the non-contractible component of the free loop space on RPnRPn.