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

By V. Bangert, Y. Long. 2007

124 citations recorded by the source corpus.

In this paper, we prove that for every Finsler metric on S2 there exist at least two distinct prime closed geodesics.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/46607faa44feed7ff2b04a2003991269fd6ef41f

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In Applied Mathematics

1. Basak Z. Gurel
2. Huagui Duan
3. Wei Wang
4. Y. Long
5. V. Ginzburg
6. Xijun Hu
7. Otto van Koert
8. Urs Frauenfelder

In Astronomy and Astrophysics

1. Huagui Duan
2. Wei Wang
3. Y. Long
4. Basak Z. Gurel
5. V. Ginzburg
6. Otto van Koert
7. Xijun Hu
8. Urs Frauenfelder

Citations in the corpus

• The Restricted Three-Body Problem and Holomorphic Curves (2018, background): “Lee’s result implies that below the first critical value the regularized energy hypersurfaces of Hill’s lunar problem are Finsler and in this case the existence of two closed characteristics was already proved by Bangert and Long [10].”
• Multiple closed geodesics on 3-spheres (2009, methodology): “10 can be found in [38] of 1992, and are similar to those contained in later papers like [3,10], and [31], we omit them here.”
• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2015, background): “c condition, and our above theorems give generic results on the above mentioned manifolds. (ii) Based on our above theorems, the works [HWZ1] in 1998 and [HWZ2] in 2003 of Hofer, Wysocki and Zehnder, [BaL] in 2010 of Bangert and Long, [LoW] in 2007 of Long and Wang, and other results mentioned above”
• Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces (2007, background): “) = DN(θ·u) ∩Γ(ι). (3.29) For a Zm-space pair (A,B), let H∗(A,B)±Zm = {σ∈ H∗(A,B)|L∗σ= ±σ}, (3.30) where Lis a generator of the Zm-action. Then by Lemma 3.8, as in Section 6 of [Rad2] or Section 3 of [BaL1], we have Lemma 3.9. Suppose u6= 0 is a critical point of Ψa with mul(u) = mand suppose Γ(ι) i”
• Lusternik–Schnirelmann theory and closed Reeb orbits (2016, methodology): “orbits on S3 and ST∗S2 is a very particular case of the theorem from [CGH] mentioned above. This result was also proved, specifically for S3 and ST∗S2, in [GH2M, GGo, LL] by different methods; see also [BL] for the case of Finsler metrics on S2. When n≥ 3, the multiplicity conjectures are completely o”