发表机构
Università di Bologna; KTH - Royal Institute of Technology（博洛尼亚大学; 皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在紧致曲面上发展Cherry流的高亏格对应物，构造满足Keane性质的$C^\fty$ Cherry流族，实现带平坦片的GIET并支撑对应数量的遍历不变测度，为相关动力系统研究提供了最优参数化方案。
AI 中文摘要
Cherry流是二维环面上具有非平凡回复动力学的经典$C^\fty$流实例。我们在紧致曲面上发展其高亏格对应物，其中带平坦片的广义区间交换变换（GIET）自然作为首次返回映射出现。我们构造$C^\fty$ Cherry流族，在半共轭意义下实现每个满足Keane性质且其组合学与曲面拓扑兼容的区间交换变换。特别地，对每个亏格$g$、每个给定的鞍指标集合及每个$k=1,\boldsymbol{\boldsymbol{}},g$，我们得到一个Cherry流，其唯一的拟极小集恰好支撑$k$个遍历不变测度。该构造背后的一维机制是带平坦片的GIET的全族定理，它在有限维参数族内实现每个容许的Rauzy重整化路径，且参数数量最优。
英文摘要
Cherry flows are classical examples of $C^\infty$ flows on the two-dimensional torus exhibiting non-trivial recurrent dynamics. For every genus $g\geq1$ we construct a $C^\infty$ parameter family of flows whose first return map is a generalized interval exchange transformation (GIET) with flat pieces. In such family, for every interval exchange transformation $T$ satisfying the Keane property, there are parameters corresponding to a Cherry flow whose return map is semi-conjugate to $T$. In particular, for each $k=1,\ldots,g$, our family contains a Cherry flow whose unique quasi-minimal set supports exactly $k$ ergodic invariant measures. The construction relies on a Full Family Theorem for GIETs with flat pieces, which establishes the realization of every admissible Rauzy renormalization path within a specific finite-dimensional family with the optimal number of parameters.
Comments51 Pages, 5 figures. Minor revisions
