区间平移映射及若干推广的混合性缺失
动力系统
2021-12-16 v2
摘要
我们考虑分段单调映射,证明对于该映射几乎处处可逆的遍历测度不可能具有混合性。由此可知,区间平移映射的任意遍历测度均非混合。我们还证明无周期点的双重旋转具有遍历但非弱混合的不变测度。本文献给 Anatoly Mikhailovich Stepin 的记忆。
引用
@article{arxiv.2102.05904,
title = {Absence of mixing for interval translation mappings and some generalizations},
author = {Serge Troubetzkoy},
journal= {arXiv preprint arXiv:2102.05904},
year = {2021}
}
备注
The proof of Lemma 6 contains a gap. Since all the results in this article are based on this lemma none of them have been established. A version of Lemma 6 with the same gap was used in (Kryzhevich, Invariant measures for interval translations and some other piecewise continuous maps, Math. Model. Nat. Phen. 15 (2020)) and thus some of the results of this article have also not been established