论文标题
向量场和lefschetz编号的分解
Resolvent of vector fields and Lefschetz numbers
论文作者
论文摘要
诸如Ruelle Zeta功能之类的动力学系列已成为双曲线流研究的主食。通常，通过将它们与向量场的分解联系起来来分析它们。在本文中，我们给出了这种关系的一般形式，涉及上述分解与集成电流的交集。我们的公式实际上对任何平滑流动，不一定是双曲线有效。作为一个应用程序，我们介绍了以前从未出现过的某些动力系列。最后，我们计算其价值为零，以及它们与拓扑不变的关系。
Dynamical series such as the Ruelle zeta function have become a staple in the study of hyperbolic flows. They are usually analyzed by relating them to the resolvent of the vector field. In this paper we give the general form of such relations, which involves the intersection of the kernel of said resolvent with integration currents. Our formula is actually valid for any smooth flow, not necessarily hyperbolic. As an application, we introduce certain dynamical series that had not appeared before. Finally, we compute their value at zero, and their relation with topological invariants.
