论文标题
环环同构的周期性轨道数量的增长和在Riemannian或Finsler上的非摘要封闭地球学的增长
The growth of the number of periodic orbits for annulus homeomorphisms and non-contractible closed geodesics on Riemannian or Finsler $\mathbb{R}P^2$
论文作者
论文摘要
在本文中，我们给出了作者\ cite {lwy}获得的Franks类型定理中周期性轨道数量的增长率。作为应用程序，我们证明了以下两个结果：在$ \ mathbb {r} p^2 $上存在无限的许多独特的非摘要闭合大地测量学，并带有riemannian指标，因此其高斯曲率是积极的，以至于其高度，超过$ \ leq l $ $ grow l^2 $ l^2 $ lengus lengvent of lengver并且存在两个或无限的许多明显的不扣除封闭的大地测量学上的$ \ mathbb {r} p^2 $，带有可逆性$λ$和flag曲率$ k $满足$ \ left（\fracλ{\fracλ{1+λ}} \ right） $ \ leq l $至少喜欢$ l^2 $。
In this article, we give a growth rate about the number of periodic orbits in the Franks type theorem obtained by the authors \cite{LWY}. As applications, we prove the following two results: there exist infinitely many distinct non-contractible closed geodesics on $\mathbb{R}P^2$ endowed with a Riemannian metric such that its Gaussian curvature is positive, moreover, the number of non-contractible closed geodesics of length $\leq l$ grows at least like $l^2$; and there exist either two or infinitely many distinct non-contractible closed geodesics on Finsler $\mathbb{R}P^2$ with reversibility $λ$ and flag curvature $K$ satisfying $\left(\fracλ{1+λ}\right)^2<K\le 1$, furthermore, if the second case happens, then the number of non-contractible closed geodesics of length $\leq l$ grows at least like $l^2$.
