Multiple closed geodesics on Finsler $3$-dimensional sphere
Symplectic Geometry
2024-01-30 v2 Differential Geometry
Dynamical Systems
Abstract
In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on 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 . In this paper, we proved this conjecture for bumpy Finsler if the Morse index of any prime closed geodesic is nonzero.
Keywords
Cite
@article{arxiv.2309.00211,
title = {Multiple closed geodesics on Finsler $3$-dimensional sphere},
author = {Huagui Duan and Zihao Qi},
journal= {arXiv preprint arXiv:2309.00211},
year = {2024}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:1504.07007