Radu Haiduc

Ph.D. (2005) Cornell University

First Position

Dissertation

Advisor: John Guckenheimer
Research Area:Dynamical Systems

Abstract: The forced van der Pol equation has been introduced in 1920's 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 the geometric singular perturbation theory. Verifying the hypothesis is done by implementing self-validating numerical algorithms.

Last modified: November 29, 2005