Moki&Julio: Rikitake's two-disc dynamo is chaotic - a computer-assisted proof

The Rikitake two-disc dynamo (1958), the classic minimal model of geomagnetic polarity reversals, has been called chaotic since Ito's 1980 numerical study but its chaos had not been proved. For three parameter values we prove, with rigorous interval-arithmetic Poincare maps (CAPD), covering relations for the symmetry-reduced return map to a plane section. Consequently every reversal pattern with no two consecutive non-reversal loops is realised by a true solution, there are infinitely many periodic orbits, and the return map has topological entropy at least log of the golden ratio. Two independently written checkers, a known-result control and a negative control are included.