论文标题
测量流的条形码熵
Barcode entropy of geodesic flows
论文作者
论文摘要
我们介绍并研究了封闭的riemannian歧管的测量流的条形码熵，该流量衡量了能量功能的摩尔斯理论条件中不短短条形条的指数生长速率。我们证明，条形码熵从测量流的拓扑熵下方，相反，从任何双曲线紧凑型不变套件的拓扑熵上方的边界。结果，对于在表面上的Riemannian指标，条形码熵等于拓扑熵。证明和独立关注的关键是能量功能的梯度流量线的交叉能量定理。
We introduce and study the barcode entropy for geodesic flows of closed Riemannian manifolds, which measures the exponential growth rate of the number of not-too-short bars in the Morse-theoretic barcode of the energy functional. We prove that the barcode entropy bounds from below the topological entropy of the geodesic flow and, conversely, bounds from above the topological entropy of any hyperbolic compact invariant set. As a consequence, for Riemannian metrics on surfaces, the barcode entropy is equal to the topological entropy. A key to the proofs and of independent interest is a crossing energy theorem for gradient flow lines of the energy functional.
