NONLINEAR SYMMETRICAL SYSTEMS

Non-oscillation, essential for control and computing systems, is secured with respect to all constitutive relations and parameter values, for multi-dimensional symmetrical systems. This applies to both discrete and continuous systems. Geometry-governed selection rules determine the admittance of solutions of a given form by a given class of eigenvalues. Existence theorems and structural stability fail together. The change of the function basis leads to an equivalent potential but may simplify the selection rules. Symmetry in the physical and phase spaces is correlated. The action of the group that leaves the equations and the boundary conditions invariant, defines an equivalence relation on the set of bifurcating solutions. The indistinguishability of the equivalent solutions is discussed. Solutions are visualized through their nodal patterns and duality relations are established. © 1979 Taylor & Francis Group, LLC.