Rigorous Study of the Chua´s Circuit Spiral Attractor

It is shown that a certain set is positively invariant for the return map associated with the Chua´s circuit. The set contains the intersection of the numerically observed spiral attractor and the planes defining the return map. A method for rigorous integration of piece-wise linear systems in regions containing trajectories tangent to hyperplanes separating the linear regions necessary to carry out the proof is developed.