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.