无理中性吸引子的拓扑
动力系统
2025-05-19 v5 泛函分析
数论
摘要
我们研究一类具有无理中性不动点的全纯系统的后临界集。我们证明了基于不动点处旋转数的算术性质的后临界集拓扑的三分法。仅有的选项是Jordan曲线、单侧多毛Jordan曲线和Cantor束。这解释了当变化旋转数时Siegel盘内闭不变曲线的退化。
引用
@article{arxiv.1706.02678,
title = {Topology of irrationally indifferent attractors},
author = {Davoud Cheraghi},
journal= {arXiv preprint arXiv:1706.02678},
year = {2025}
}
备注
53 pages, 10 figures. Revisions following referee reports. The original preprint under this tile is now divided into two papers. The first part of the paper on the model now appears as arXiv:2112.14557