The existence of two closed geodesics on every Finsler 2-sphere

2007/09/09 by Victor Bangert, Bangert, Victor, Yiming Long +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #37J45 #53C22 #58E05 #58E10 #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Fibroblast Growth Factor Research #Geometric Analysis and Curvature Flows #Symplectic Geometry (math.SG) #math.DS #math.SG #msc:37J45 #msc:53C22 #msc:58E05 #msc:58E10

paper · pdf · doi:10.48550/arxiv.0709.1243

36 pages, 1 figure, added a remark before Theorem 1.1

openalex publication_date 2007/09/09 · arxiv created 2007/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that for every Finsler metric on the 2-dimensional sphere there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem posed by D. V. Anosov in 1974.

Citations

• Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders

Related

• The second closed geodesic on Finsler spheres of dimension n>2
• Multiple closed geodesics on Finsler 3-dimensional sphere
• Existence of closed geodesics on Finsler n-spheres
• Two closed geodesics on compact bumpy Finsler manifolds
• Two short closed geodesics on a sphere of odd dimension