Geodesic
Geometry and arithmetic of verbal dynamical systems on simple groups
Tatiana Bandman1 ; Fritz Grunewald2 ; Boris Kunyavskii1 ; Nathan Jones3
1Bar-Ilan University, Ramat Gan, Israel
2Heinrich-Heine-Universität, Düsseldorf, Germany
3University of Mississippi, USA
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 607-655

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DOI

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.
DOI : 10.4171/ggd/98
Classification : 14-XX, 20-XX, 00-XX
Mots-clés : Solvable group, word map, trace map, dynamical system, periodic point, elliptic curve

Tatiana Bandman  1   ; Fritz Grunewald  2   ; Boris Kunyavskii  1   ; Nathan Jones  3

1 Bar-Ilan University, Ramat Gan, Israel
2 Heinrich-Heine-Universität, Düsseldorf, Germany
3 University of Mississippi, USA 
Tatiana Bandman; Fritz Grunewald; Boris Kunyavskii; Nathan Jones. Geometry and arithmetic of verbal dynamical systems on simple groups. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 607-655. doi: 10.4171/ggd/98
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     year = {2010},
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     doi = {10.4171/ggd/98},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/98/}
}
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