随机阿诺德猜想：辛映射的新概率性 Conley-Zehnder 理论
动力系统
2023-08-01 v2 概率论
辛几何
摘要
我们迈出了在概率世界中发展由阿诺德所猜想的 Conley-Zehnder 理论的第一步。据我们所知，本文给出了关于维数大于 的辛扭转映射不动点密度的首批概率性定理。特别地，我们将证明，当经典 Conley-Zehnder 理论的类比条件成立时，准周期辛扭转映射几乎必然具有无穷多个不动点。本文还包含若干远超准周期情形的定理。
引用
@article{arxiv.2306.15586,
title = {The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps},
author = {Álvaro Pelayo and Fraydoun Rezakhanlou},
journal= {arXiv preprint arXiv:2306.15586},
year = {2023}
}
备注
54 pages. Some partial results have been strengthened, overall presentation improved, several examples and connections with other subjects have been added and made explicit, further motivations included