Non-hyperbolic closed geodesics on positively curved Finsler spheres

Abstract

In this paper, we prove that for every Finsler $n$-dimensional sphere $(S^n,F),n\ge 3$ with reversibility $\lambda$ and flag curvature $K$ satisfying ${\left(\frac{\lambda }{1+\lambda }\right)}^2<K\le 1$, there exist at least three distinct closed geodesics and at least two of them are elliptic if the number of prime closed geodesics is finite. When $n\ge 6$, these three distinct closed geodesics are non-hyperbolic.

Revised submission. arXiv admin note: substantial text overlap with arXiv:1504.00245; text overlap with arXiv:0705.4190, arXiv:1112.5234, arXiv:0909.3566, arXiv:0812.0039 by other authors

References in corpus (4)

• Multiple closed geodesics on bumpy Finsler $n$-spheres
• Two elliptic closed geodesics on positively curved Finsler spheres
• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
• Closed geodesics on positively curved Finsler spheres

Cited by in corpus (1)

• Existence results for closed Finsler geodesics via spherical complexities