Horseshoes in the forced van der Pol system

The forced van der Pol equation was introduced in the 1920s as a model of an electrical circuit. Cartwright and Littlewood established the existence of invariant sets with complex topology in this system. This paper contains, for the first time, a full description of the nonwandering set for an open set of parameters near the singular limit of the forced van der Pol equation. In particular, we prove the existence of a hyperbolic chaotic invariant set. We also prove that the system is structurally stable. The analysis is conducted from the perspective of geometric singular perturbation theory. Verifying the hypothesis is done by implementing self-validating numerical algorithms.