1999/01/27 by Michael Baake, Baake, Michael, John A G Roberts +2
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.math/9901124
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
arxiv created 1999/01/27 · openalex publication_date 1999/01/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).