一般连续保 Lebesgue 测度的区间映射在 nowhere 单调但几乎处可逆
动力系统
2026-02-06 v3
摘要
我们考察保 Lebesgue 测度的区间连续映射。除恒等映射或 外，这类映射的拓扑熵至少为 ，且一般具有无限拓扑熵。本文证明了一般映射具有零测度论熵。这意味着在拓扑与测度行为上存在显著差异，包括单射性以及一般映射层集结构。作为推论，我们得到了一组与伪弧同胚的平面吸引子的惊人结果。
关键词
引用
@article{arxiv.2405.09917,
title = {Generic continuous Lebesgue measure-preserving interval maps are nowhere monotone but invertible a.e},
author = {Jozef Bobok and Jernej Činč and Piotr Oprocha and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:2405.09917},
year = {2026}
}
备注
1) The title has changed, the introduction has been reorganized and section 5 has been added, in this section we give an application to planar attractors.2) Minor changes after referee report, the article will appear in Studia Mathematica