arXiv:1306.0821 Abstract | arXiv Analytics

arXiv:1306.0821 [math.DS]Abstract References Reviews Resources

Poincaré-Birkhoff theorems in random dynamics

Published 2013-06-04, updated 2014-12-06Version 2

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.

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

Categories: math.DS, math.PR, math.SG

Keywords: random dynamics, poincaré-birkhoff theorems, poincare-birkhoff theorem states, ergodic probability measure, area-preserving periodic twist map

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