Arnoux-Yoccoz 曲面的 Rel 叶
动力系统
2020-02-24 v4
摘要
我们分析了 Arnoux-Yoccoz 平移曲面的 rel 叶。我们证明，对于任意亏格 ，该叶在其所属的层 的连通分支中是稠密的，并且该曲面的单侧虚部 rel 轨迹是发散的。对于该轨迹上的一个曲面，即 Arnoux-Yoccoz 曲面本身，其水平叶状结构在伪 Anosov 映射下是不变的（并且特别地是唯一遍历的），但对于所有其他曲面，水平叶状结构是完全周期的。附录证明了该叶稠密性所需的一个域论结果：对于任意 ，通过添加 的根得到的扩张有理数域，除了有理数域外没有全实子域。
引用
@article{arxiv.1508.05363,
title = {Rel leaves of the Arnoux-Yoccoz surfaces},
author = {W. Patrick Hooper and Barak Weiss},
journal= {arXiv preprint arXiv:1508.05363},
year = {2020}
}
备注
Appendix by Lior Bary-Soroker, Mark Shusterman and Umberto Zannier. The prior version was published, but had errors in \S 6. Erroneous statements have been indicated and an erratum was included as Appendix B which corrects the errors. Main results are still correct. 70 pages, 9 figures. arXiv admin note: text overlap with arXiv:1506.06773