AI 中文总结
本文证明C¹流的多奇异双曲集为Komuro扩张的，借此建立周期轨道的渐近计数界，证明归一化轨道测度收敛到最大熵测度，还对星型向量场的C¹开稠密子集得到相同结论。
AI 中文摘要
本文证明，C¹流的每个多奇异双曲集都是Komuro扩张的，这是正则轨道积累奇点的流的最强自然扩张形式，允许任意保定向时间重参数化。随后利用该结论建立周期轨道的e^(ht)/t形式的双侧渐近计数界，并证明归一化轨道测度收敛到唯一的最大熵测度，还对星型向量场的C¹开稠密子集建立了相同结果。
英文摘要
In this paper we prove that every multi-singular hyperbolic set of a $C^1$ flow is Komuro expansive. This is the strongest natural form of expansivity for flows with singularities accumulated by regular orbits, allowing arbitrary orientation-preserving time reparametrizations. We then use this to establish a two-sided asymptotic counting bound of the form $e^{ht}/t$ for periodic orbits, and prove that the normalized orbit measures converge to the unique measure of maximal entropy. We also establish the same results for a $C^1$ open and dense subset of star vector fields.
Comments49 pages and 3 figures
