Geometry and arithmetic of verbal dynamical systems on simple groups

Tatiana Bandman; Fritz Grunewald; Boris Kunyavskiǐ; Nathan Jones

doi:10.4171/GGD/98

Geometry and arithmetic of verbal dynamical systems on simple groups

Tatiana Bandman, Fritz Grunewald, Boris Kunyavskiǐ, Nathan Jones

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English
Pages (from-to)	607-655
Number of pages	49
Journal	Groups, Geometry, and Dynamics
Volume	4
Issue number	4
DOIs	https://doi.org/10.4171/GGD/98
State	Published - 2010

Keywords

Dynamical system
Elliptic curve
Periodic point
Solvable group
Trace map
Word map

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10.4171/GGD/98

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Geometry and arithmetic of verbal dynamical systems on simple groups

Abstract

Keywords

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