Symmetries and Reversing Symmetries of Trace Maps
نویسندگان
چکیده
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).
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