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.

36 pages, 1 figure, added a remark before Theorem 1.1