JournalsggdVol. 4, No. 4pp. 607–655

Geometry and arithmetic of verbal dynamical systems on simple groups

  • Tatiana Bandman

    Bar-Ilan University, Ramat Gan, Israel

  • Fritz Grunewald

    Heinrich-Heine-Universität, Düsseldorf, Germany

  • Boris Kunyavskii

    Bar-Ilan University, Ramat Gan, Israel

  • Nathan Jones

    University of Mississippi, USA
Geometry and arithmetic of verbal dynamical systems on simple groups cover
Download PDF

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 this article

Tatiana Bandman, Fritz Grunewald, Boris Kunyavskii, Nathan Jones, Geometry and arithmetic of verbal dynamical systems on simple groups. Groups Geom. Dyn. 4 (2010), no. 4, pp. 607–655

DOI 10.4171/GGD/98