发表机构
Hangzhou International Innovation Institute of Beihang University（北京航空航天大学杭州创新研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对度量空间上的流，证明紧度量空间上流的有限拓扑熵由正则集紧子集承载，建立Bowen–Walters不等式并将其应用于多类奇异流，扩展了相关文献的结论。
AI 中文摘要
我们研究度量空间上流的熵与周期轨道增长。首先，证明紧度量空间上流的有限拓扑熵完全由其正则集的紧子集承载。其次，针对可能非紧的度量空间上的几何分离流，建立Bowen–Walters不等式，条件为零时刻的一致控制与无穷远的动力学隔离。作为应用，得到膨胀同胚上的奇异悬挂流、多奇异双曲集（扩展了文献[pyyz]的上界部分）及渐近截面双曲吸引子（如Rovella的文献[r]）的Bowen–Walters不等式。
英文摘要
We study entropy and periodic-orbit growth for flows on metric spaces. First, we prove that the finite topological entropy of a flow on a compact metric space is completely carried by compact subsets of its regular set. Next, we establish a Bowen--Walters inequality for geometrically separating flows on possibly noncompact metric spaces, under uniform control at time zero and dynamical isolation at infinity. As applications, we obtain the Bowen--Walters inequality for singular suspension flows over expansive homeomorphisms, multisingular-hyperbolic sets---extending the upper-bound part of \cite{pyyz}---and asymptotically sectional-hyperbolic attractors such as Rovella's \cite{r}.
Comments19 pages
