Multiple closed geodesics on Finsler 3-dimensional sphere

2023/09/01 by Huagui Duan, Zihao Qi, Duan, Huagui +1
Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2309.00211

openalex publication_date 2023/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on S³ with exactly four prime closed geodesics. And then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler S³. In this paper, we proved this conjecture for bumpy Finsler S³ if the Morse index of any prime closed geodesic is nonzero.

Related

• Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres
• The second closed geodesic on Finsler spheres of dimension n>2
• The existence of two closed geodesics on every Finsler 2-sphere
• Two short closed geodesics on a sphere of odd dimension
• The index growth and multiplicity of closed geodesics