Uniformly hyperbolic attractor of the Smale-Williams type for a Poincar\'e map in the Kuznetsov system

Abstract

We propose a general algorithm for computer assisted verification of uniform hyperbolicity for maps which exhibit a robust attractor. The method has been successfully applied to a Poincare map for a system of coupled non-autonomous van der Pol oscillators. The model equation has been proposed by Kuznetsov and the attractor seems to be of the Smale-Williams type.