论文标题
Franks定理和REEB动态应用程序的改进
Refinements of Franks' theorem and applications in Reeb dynamics
论文作者
论文摘要
在本文中，我们给出了Franks定理的两种改进：为了定向和区域保存封闭或开放环的同构，存在$ k $ - 周期性轨道（$（$（k，n_0）= 1 $），迫使存在无限的多个周期性的典型轨道，这些期刊具有元素至$ $ n_0 $。此外，如果$ f $是可逆的，则上述周期性轨道可能是对称的。例如，我们改善弗兰克斯定理的改进可以应用于REEB动力学和天体力学，我们提供了一些精确的信息，以了解Hofer，Wysocki和Zehnder的二分法定理中周期性轨道的对称性，当时紧密的3-Sphere配备了一些附加的符号级别，以及对周期性或周期性或周期性或周期性的层次时， h $ \急性{e} $ non-Heiles系统中的天体力学。
In this article, we give two refinements of Franks' theorem: For orientation and area preserving homeomorphisms of the closed or open annulus, the existence of $k$-periodic orbits ($(k,n_0)=1$) forces the existence of infinitely many periodic orbits with periods prime to $n_0$. Moreover, if $f$ is reversible, the periodic orbits above could be symmetric. Our improvements of Franks' theorem can be applied to Reeb dynamics and celestial mechanics, for example, we give some precise information about the symmetries of periodic orbits found in Hofer, Wysocki and Zehnder's dichotomy theorem when the tight 3-sphere is equipped with some additional symmetries, and also the symmetries of periodic orbits on the energy level of H$\acute{e}$non-Heiles system in celestial mechanics.
