Symmetry breaking and fractal dependence on initial conditions in dynamical systems: Ordinary differential equations of thermal convection
The authors investigate a three-dimensional dynamical system having co-existing attractors with complicated basin boundaries, which describes thermal convection in fluids. It is shown that the boundary structure, after symmetry breaking, is determined by stable manifolds of symmetric repellers. Geometry of a basin boundary formed in regular dynamic regime is explained and shown to be quasi-fractal.
scientific article; zbMATH DE number 1370458
scientific article