发表机构
Universidade Federal de Pernambuco（巴西联邦伯南布哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究具有无理圆周因子的环面同胚，在纤维为Jordan曲线等条件下证明极小集唯一性，并构造具有多个极小Cantor集的例子。
AI 中文摘要
我们研究环面同胚的极小集，这些同胚具有无理圆周因子，其纤维是薄的本质环状连续统。对于完全无理伪旋转和非平凡Dehn-twist类中的同胚，我们证明了当纤维在基参数的剩余集上是Jordan曲线时，极小集的唯一性。如果纤维核是Jordan曲线，或者纤维是局部连通的，在参数的不可数集上，同样的结论也成立。剩余假设不能被全测度假设所取代，即使在保面积和拓扑传递的情况下也是如此。对于每一个完全无理旋转向量，我们构造了这样的映射，其Jordan曲线纤维几乎处处存在，并且存在不可数多个两两不相交的唯一遍历极小Cantor集。我们还在每个非平凡Dehn-twist类中构造了例子，具有指定的无理垂直旋转数和有界偏差。在这两个族中，Jordan曲线参数形成一个全Lebesgue测度的剩余集。
英文摘要
We study minimal sets of torus homeomorphisms admitting an irrational circle factor whose fibres are thin essential annular continua. For totally irrational pseudo-rotations and homeomorphisms in a nontrivial Dehn-twist class, we prove uniqueness of the minimal set when the fibres are Jordan curves on a residual set of base parameters. The same conclusion holds if the fibre cores are Jordan curves, or if the fibres are locally connected, on a nonmeagre set of parameters. The residual hypothesis cannot be replaced by a full-measure hypothesis, even under area preservation and topological transitivity. For every totally irrational rotation vector, we construct such a map with Jordan-curve fibres almost everywhere and uncountably many pairwise disjoint uniquely ergodic minimal Cantor sets. We also construct examples in every nontrivial Dehn-twist class, with prescribed irrational vertical rotation number and bounded deviations. In both families, the Jordan-curve parameters form a meagre set of full Lebesgue measure.
