BIFURCATION AND CHAOS IN ITERATED MAPS WITH O(2) SYMMETRY

Iterated maps with O(2) symmetry are considered with a view to understanding transitions which occur as a parameter is varied. Bifurcations from the trivial solution are first considered followed by secondary bifurcations from nontrivial solutions. This is achieved by the derivation of a new system of equations in the orbit space. A transition in which a symmetric chaotic attractor starts drifting round the group orbit is also considered and it is shown that a single antisymmetric Lyapunov exponent determines whether or not a symmetric attractor is stable to nonsymmetric perturbations.