Controlling chaos in systems with \(O(2)\) symmetry (Q1809586)

Continuous symmetries of a system, in this case \(O(2)\), makes hyperbolicity of fixed points impossible. The author considers the orbit space of the group action and can apply known results on the stabilization of hyperbolic fixed points. For instance small parameter changes can stabilize saddle points in chaotic attractors of systems with \(O(2)\) symmetry.