Poincaré-Birkhoff theorems in random dynamics

Abstract

We propose a generalization of the Poincaré-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.

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