%0 Journal Article
%T Geometry and arithmetic of verbal dynamical systems on simple groups
%A Tatiana Bandman
%A Fritz Grunewald
%A Boris Kunyavskii
%A Nathan Jones
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0809.0369v2