Computer Assisted Proofs of Contracting Invariant Tori for ODEs

Maciej J. Capinski, Emmanuel Fleurantin, Jason D. Mireles James

Published 2019-05-20Version 1

This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which applies to explicit problems in non-perturbative regimes. We obtain verifiable bounds on the regularity of the attractor in terms of the ratio of the expansion rate on the torus with the contraction rate near the torus. We consider separately two important cases of rotational and resonant dynamics on the torus. In the resonant case we obtain the existence of tori which are $C^0$ but not Lipschitz.