论文标题
计算矢量场的周期性轨道上的光滑封闭歧管
Counting periodic orbits of vector fields over smooth closed manifolds
论文作者
论文摘要
我们解决了在光滑的封闭歧管上计数矢量场周期轨道的问题。非恒定周期轨道的空间通过添加幽灵轨道（即矢量场的零件的装饰），将其放大到一个完整的空间。与周期性和幽灵轨道的模量空间的任何紧凑和开放子集$γ$相关联，我们定义了整数重量。当矢量场沿路径移动，而$γ$在紧凑和开放的家族中变形时，我们表明重量函数保持恒定。我们还提供了许多示例和计算，这些示例和计算说明了我们的主要定理的应用。
We address the problem of counting periodic orbits of vector fields on smooth closed manifolds. The space of non-constant periodic orbits is enlarged to a complete space by adding the ghost orbits, which are decorations of the zeros of vector fields. Associated with any compact and open subset $Γ$ of the moduli space of periodic and ghost orbits, we define an integer weight. When the vector field moves along a path, and $Γ$ deforms in a compact and open family, we show that the weight function stays constant. We also give a number of examples and computations, which illustrate the applications of our main theorem.
