格罗莫夫-瑟斯顿流形与分支覆盖的熵
The entropy of Gromov-Thurston manifolds and branched coverings
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中文总结 AI 辅助
该研究建立局部CAT(k)分支覆盖测地流动力学的一般理论，推导其熵的显式公式，得到熵随分支覆盖片数趋于无穷的渐近及最大熵测度的渐近性质。
中文摘要 AI 辅助
我们建立了局部CAT(k)分支覆盖的测地流动力学的一般理论，证明其不依赖于具体的覆盖，仅取决于基空间、分支集和覆盖次数。我们得到了熵的显式公式：它等于关联自然动力系统在带自然几何势的断裂测地线路径空间上的拓扑压力。我们还得到了当分支覆盖的片数趋于无穷时熵的精确渐近，以及最大熵测度的渐近性质。
英文摘要
We develop a general theory for the dynamics of the geodesic flow of locally CAT(k) branched coverings and we show that it does not depend on the specific covering but only on the base space, the branching set and the degree of the covering. We find an explicit formula for the entropy: it equals the topological pressure of the associated natural dynamical system on the space of broken geodesics with a natural geometric potential. We find the exact asymptotic of the entropy as the number of sheets of the branched covering goes to infinity, as well as asymptotic properties of the measures of maximal entropy.
