Symmetries and reversing symmetries of trace maps
Abstract
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).
Keywords
Cite
@article{arxiv.math/9901124,
title = {Symmetries and reversing symmetries of trace maps},
author = {Michael Baake and John A. G. Roberts},
journal= {arXiv preprint arXiv:math/9901124},
year = {2007}
}
Comments
5 pages; originally written for the proceedings of the 3rd Intern. Wigner Symposium (Oxford, 1993); since they will not be in print this millennium (and prob. neither in the next), better download from here