论文标题
最小值的凸lagrangian系统的周期性轨道在完整的riemannian歧管上
Minimax periodic orbits of convex Lagrangian systems on complete Riemannian manifolds
论文作者
论文摘要
在本文中，我们研究了在完整的Riemannian歧管上具有凸出凸的Lagrangian系统规定能量水平的周期性轨道的存在。我们通过将修改后的Minimax主体开发到非策略Riemannian歧管上的一类Lagrangian系统，即所谓的$ \ lsh $ lagrangian Systems。特别是，我们证明，几乎每$ k \ in（0，c_u（l））$与$ \ lsh $ lagrangian相关的精确磁流，具有带能量$ k $的可签期的周期性轨道。我们还讨论了Riemannian歧管$ \ r \ r \ times m $的封闭测量学的存在和不存在。
In this paper we study the existence of periodic orbits with prescribed energy levels of convex Lagrangian systems on complete Riemannian manifolds. We extend the existence results of Contreras by developing a modified minimax principal to a class of Lagrangian systems on noncompact Riemannian manifolds, namely the so called $\lsh$ Lagrangian systems. In particular, we prove that for almost every $k\in(0,c_u(L))$ the exact magnetic flow associated to a $\lsh$ Lagrangian has a contractible periodic orbit with energy $k$. We also discuss the existence and non-existence of closed geodesics on the product Riemannian manifold $\R\times M$.
