A fixed point theorem for twist maps
Dynamical Systems
2021-06-14 v1
Abstract
Poincare's last geometric theorem (Poincare-Birkhoff Theorem) states that any area-preserving twist map of annulus has at least two fixed points. We replace the area-preserving condition with a weaker intersection property, which states that any essential simple closed curve intersects its image under at least at one point. The conclusion is that any such map has at least one fixed point. Besides providing a new proof to Poincare's geometric theorem, our result also has some applications to reversible systems.
Cite
@article{arxiv.2106.06374,
title = {A fixed point theorem for twist maps},
author = {Peizheng Yu and Zhihong Xia},
journal= {arXiv preprint arXiv:2106.06374},
year = {2021}
}