English

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.

Keywords

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

R2 v1 2026-06-21T11:15:57.962Z