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Symmetries and reversing symmetries of trace maps

Michael Baake·John A. G. Roberts
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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).

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Michael Baake, John A. G. Roberts. 1999-01-27. Symmetries and reversing symmetries of trace maps. https://arxiv.org/abs/math/9901124

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