The Crawford prize is awarded biannually since 2001 at the `Snowbird' conferences by the SIAM activity group on dynamical systems for recent outstanding work on a topic in nonlinear science. In a series of articles we invite the winners to write about their mathematical biography, their work, and what they consider important problems in the field of applied dynamical system. This article is the contribution of the Dwight Barkley, the prize winner from 2005.