An example of how the Ricci Flow can increase topological entropy

A criterion for topological entropy to decrease under normalised Ricci flow

In 2004, Manning showed that the topological entropy of the geodesic flow for a surface of negative curvature decreases as the metric evolves under the normalised Ricci flow. It is an interesting open problem, also due to Manning, to determine to what extent such behaviour persists for higher dimensional manifolds. In this short note, we describe the problem and give a strong criterion under which monotonicity of the topological entropy can be established for a short time. In particular, the criterion applies to metrics of negative sectional curvature which are in the same conformal class as a…

双曲度量附近Ricci流的拓扑熵单调性

Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric

本文解决了Manning提出的问题，证明了带双曲度量的闭黎曼流形的测地流拓扑熵，在与双曲度量足够接近的变负截面曲率度量出发的归一化Ricci流中严格递减。

曲面上的里奥维勒熵沿规范里齐流的单调性

Monotonicity of the Liouville entropy along the Ricci flow on surfaces

研究显示，在非常数负曲率闭合曲面上，规范里齐流下里奥维勒熵最终严格递增，并推导出二维任一共形变形下里奥维勒熵导数的新表达式，证明其在1/6弯曲度指标方向上为正，部分回答了曼宁2004年的问题。

极小曲面熵与 Ricci 流在有限体积双曲 3-流形上的应用

Minimal surface entropy and applications of Ricci flow on finite-volume hyperbolic 3-manifolds

本文研究有限体积双曲 3-流形上的极小曲面熵，利用曲率条件及 Ricci 流收敛速率，证明双曲度量分别对应熵的最小值或唯一最大值。

创新动力学：利用 Perelman 熵与 Ricci 流构建流形上的星体位置模型

Innovative Dynamics: Utilizing Perelman's Entropy and Ricci Flow for Settler Position Models on Manifolds

本文提出一种基于离散动力系统、Ricci 流和 Perelman 熵的恒星位置混沌建模方法，通过 Lyapunov 指数与分岔分析揭示其动力学特性，并证明熵呈指数增长导致长期位置预测难度增加。

Ricci-flat metrics and dynamics on K3 surfaces

We give an overview of some recent interactions between the geometry of K3 surfaces and their Ricci-flat Kahler metrics and the dynamical study of K3 automorphisms with positive entropy.