Reversing Symmetry Groups of Cat Maps
نویسنده
چکیده
Toral automorphisms are widely used (discrete) dynamical systems, the perhaps most prominent example (in 2D) being Arnold's cat map. Given such an automorphism M , its symmetries (i.e. all automorphisms that commute with M) and reversing symmetries (i.e. all automorphisms that conjugate M into its inverse) can be determined by means of number theoretic tools. Here, the case of Gl(2; Z Z) is presented and the possible (reversing) symmetry groups are completely classiied. Extensions to aane mappings and to k-(reversing) symmetries (i.e. (reversing) symmetries of M k), and applications to the projective group P Gl(2; Z Z) and to trace maps are brieey discussed.
منابع مشابه
Reversing symmetry group of Gl(2,Z) and PGl(2,Z) matrices with connections to cat maps and trace maps
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