$C^r$ 表面微分子动力学中最大熵鞅测度的连续性
动力系统
2025-12-01 v3
摘要
设 为 表面微分子动力学，且具有较大的熵(更准确地说，)。则该系统的熵最大鞅测度的个数在 处为上半连续的。这推广了 \cite{BCS22} 中研究的 情况，回答了该文中的问题 1.9。此外，当且仅当该系统的所有熵最大鞅测度在小扰动下都具有鞅延续时，该个数才是局部常数的。在这种情况下，熵最大鞅测度的聚点本身也是鞅测度。这些事实即使在 情况下也是全新的。
引用
@article{arxiv.2412.19658,
title = {Continuity properties of ergodic measures of maximal entropy for $C^r$ surface diffeomorphisms},
author = {Jérôme Buzzi and Chiyi Luo and Dawei Yang},
journal= {arXiv preprint arXiv:2412.19658},
year = {2025}
}
备注
35pages, 4Figures. Compared with the previous version, this one provides an equivalent characterization of the continuity of the number of ergodic MMEs and constructs examples showing that discontinuity can indeed occur. Most of these ideas originate from J\'er\^ome Buzzi, and thus we completed the writing of the paper in collaboration