Existence of closed geodesics on positively curved Finsler manifolds

By H. Rademacher. Ergodic Theory and Dynamical Systems, 2005

66 citations recorded by the source corpus.

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/56d6c1329ff93cf57a6760e0eb7b982f8858b6a7

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In Astronomy and Astrophysics

1. Huagui Duan
2. Y. Long
3. Wei Wang
4. V. Bangert
5. Basak Z. Gurel
6. V. Ginzburg

Citations in the corpus

• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2015, background): “ X) jX2TM; F(X) = 1g1: (1.2) Note that the lower bound 2[n+1 2 ] on the number of distinct closed geodesics for spheres S n is sharp due to the above mentioned examples of Katok. Besides spheres, in [Rad4], Rademacher obtained some multiplicity and stability results of closed geodesics on compact si”
• Multiple closed geodesics on 3-spheres (2009, methodology): “We are only aware of a few results on the existence of multiple closed geodesics on Finsler as well as Riemannian spheres without pinching type conditions as those used in [4,5,39], etc.”
• The existence of two closed geodesics on every Finsler 2-sphere (2007, background): “closed geodesic also follows from the recent paper [ Rad3 ] by H.-B.”