Quantifying symmetric chaos Free

Nonlinear systems exhibit features which cannot be understood, controlled, or exploited without addressing their behavior in a nonlinear form. Symmetric chaotic mappings, which were described by Field and Golubitsky [Comput. Phys. 4, 470 (1990)], comprise an interesting subclass of nonlinear systems. Field and Golubitsky described qualitative techniques for the characterization of the attractors for these mappings. Here we present qualitative and quantitative descriptions of the attractors of a number of symmetric chaotic mappings, which undergo a change of symmetry from D_n to Z_n as a parameter ω is varied.