%0 Journal Article
%T Symmetries and reversing symmetries of trace maps
%A Michael Baake
%A John A. G. Roberts
%J Mathematics
%D 1999
%I arXiv
%X A (discrete) dynamical system may have various symmetries and reversing symmetries, which together form its so-called reversing symmetry group. We study the set of 3D trace maps (obtained from two-letter substitution rules) which preserve the Fricke-Vogt invariant I(x,y,z). This set of dynamical systems forms a group G isomorphic with the projective linear (or modular) group PGL(2,Z). For such trace maps, we give a complete characterization of the reversing symmetry group as a subgroup of the group A of all polynomial mappings that preserve I(x,y,z).
%U http://arxiv.org/abs/math/9901124v1