Poincar\'e-Birkhoff theorems in random dynamics
Dynamical Systems
2014-12-09 v2 Probability
Symplectic Geometry
Abstract
We propose a generalization of the Poincar\'e-Birkhoff Theorem on area-preserving twist maps to area-preserving twist maps that are random with respect to an ergodic probability measure. The classical theory is a particular instance of the random theory we propose.
Cite
@article{arxiv.1306.0821,
title = {Poincar\'e-Birkhoff theorems in random dynamics},
author = {Álvaro Pelayo and Fraydoun Rezakhanlou},
journal= {arXiv preprint arXiv:1306.0821},
year = {2014}
}
Comments
35 pages, 5 figures. Presentation improved and added a new appendix explaining the relation between the classical theory and the random theory proposed in this paper