Symmetry Breaking and Fractal Dependence on Initial Conditions in Dynamical Systems: Ordinary Differential Equations of Thermal Convection

A system of n = 3 ordinary differential equations with discrete symmetry describing thermal convection in fluids is investigated. It is shown that the boundary structure of basins of co-existing, non-symmetric attractors, which are present after symmetry breaking, is determined by stable manifolds of the symmetric repellers. Moreover, boundary components fall into two classes: separating boundaries, dim(WS) = n−1, or non-separating boundaries, dim(WS)