Geometry and arithmetic of verbal dynamical systems on simple groups

Tatiana Bandman, Fritz Grunewald, Boris Kunyavskiǐ, Nathan Jones

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 languageEnglish
Pages (from-to)607-655
Number of pages49
JournalGroups, Geometry, and Dynamics
Issue number4
StatePublished - 2010


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


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