On the Symmetry-Breaking Bifurcation of Chaotic Attractors
Symmetry breaking is a common phenomenon in nature. (1) In the field of dynamical systems, the symmetry-breaking bifurcation of attractors is a subject of special interest. For limit cycles this phenomenon has been studied extensively, (a) especially in the Lorenz model. (3) Less is known about the symmetry breaking of chaotic attractors. A symmetry-recovering crisis has been discovered experimentally and modeled in ref. 4. Here we consider the symmetry breaking of strange attractors from another point of view in a more general class of systems and we show that a new type of crisis (5) may exist leading to an anomalous band splitting (6) or to a symmetry-breaking transition of the strange attractor, depending on the actual values of the parameters. We investigate Lorenz-type systems characterized by the property that trajectories on the attractor pass close to a saddle point. This saddle has a two-dimensional stable and a one-dimensional unstable invariant manifold. Therefore, trajectories approaching the stable manifold may stay for an
Symmetry-breaking bifurcations in O(2) maps
Codimension-one bifurcations of O(2)-equivariant maps on Rn are analyzed. Steady-state and period-doubling bifurcations lead to reflection symmetric patterns; subsequent instabilities can lead to a slow phase precession. For Hopf bifurcation, the theory for steady-state bifurcation with D4-symmetry applies.
Investigating the Optical properties of cd1-xznxs thin films deposited by the Dip Technique
A Thesis submitted to the Department of Physics, Kwame Nkrumah University of Science and Technology, in partial fulfillment of the requirement for the degree of 
Master of Science (Solid State Physics)