On a conjecture of Anosov

Wei Wang

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arXiv · 1112.5234

On a conjecture of Anosov

Wei Wang

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Abstract

In this paper, we prove that for every bumpy Finsler $n$-sphere $(S^n,\,F)$ with reversibility $λ$ and flag curvature $K$ satisfying $(\fracλ{λ+1})^2<K\le 1$, there exist $2[\frac{n+1}{2}]$ prime closed geodesics. This gives a confirmed answer to a conjecture of D. V. Anosov \cite{Ano} in 1974 for a generic case.

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Wei Wang. 2011-12-23. On a conjecture of Anosov. https://arxiv.org/abs/1112.5234

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