AI 中文总结
研究广义区间交换变换或实直线上康托子集的局部单调同胚，证明间断点数有界、共轭于特定同胚限制、在相应群中扭曲这三个条件等价。
AI 中文摘要
设f为广义区间交换变换或实直线上康托子集的局部单调同胚。本文证明了以下条件等价：1. f^n的间断点数有界；2. 存在n≥1，使得元素f共轭于该n个不交并圆同胚在一个闭不变子集上的限制；3. 元素f在广义区间交换变换群或康托子集的局部单调同胚群中是扭曲的。
英文摘要
Let f be either a generalized interval exchange transformation or a locally monotone homeomorphism of a Cantor subset of the real line. In this article, we prove that the following are equivalent. 1. The number of discontinuities of f^n is bounded. 2. There exists n $\ge$ 1 such that the element f is conjugate to the restriction to a closed invariant subset of a disjoint union of n circles of a homeomorphism of this disjoint union of circles. 3. The element f is distorted in the group of generalized interval exchange transformations or in the group of locally monotone homeomorphisms of the Cantor subset.
