Geometry and arithmetic of verbal dynamical systems on simple groups
Algebraic Geometry
2009-09-29 v2 Dynamical Systems
Abstract
We study dynamical systems arising from word maps on simple groups. We develop a geometric method based on the classical trace map for investigating periodic points of such systems. These results lead to a new approach to the search of Engel-like sequences of words in two variables which characterize finite solvable groups. They also give rise to some new phenomena and concepts in the arithmetic of dynamical systems.
Cite
@article{arxiv.0809.0369,
title = {Geometry and arithmetic of verbal dynamical systems on simple groups},
author = {Tatiana Bandman and Fritz Grunewald and Boris Kunyavskii and Nathan Jones},
journal= {arXiv preprint arXiv:0809.0369},
year = {2009}
}
Comments
35 pages; substantial revision; title changed; appendix by Nathan Jones added