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

Abstract

In this paper, we prove that for every Finsler metric on the 2-dimensional sphere there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem posed by D. V. Anosov in 1974.

arXiv comment36 pages, 1 figure, added a remark before Theorem 1.1

References in corpus (1)

• Dynamically convex Finsler metrics and $J$-holomorphic embedding of asymptotic cylinders

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