平面区域非自映射的不动点定理
动力系统
2013-05-06 v3 一般拓扑
摘要
设 和 是 中紧致、单连通且局部连通的子集，且 是 上同伦于恒等映射的同胚映射。推广 Brouwer 关于平面自映射的平面平移定理，我们证明了若 没有不动点，则 没有回归点（特别是没有周期点）。
引用
@article{arxiv.1112.3587,
title = {Fixed Point Theorem for Non-Self Maps of Regions in the Plane},
author = {Georg Ostrovski},
journal= {arXiv preprint arXiv:1112.3587},
year = {2013}
}
备注
11 pages, 5 figures; significant improvement and generalization of the result in the first version ("Jordan domains" replaced by "compact, simply connected, locally connected sets" in the assumptions of the main result)