My area of research is chaotic properties of dynamical systems. Systems that I am particularly interested include geodesic flow on surfaces and billiards.
This picture shows an unusal shaped sphere which exists in three dimensional space whose geodesic flow is ergodic. From the article by Keith Burns and Victor Donnay, Embedded surfaces with ergodic geodesic flow, Inter. J. of Bifurcation and Chaos Vol. 7, No. 7 (1997), 1509-1527.
More such pictures.
List of publications.
Together with my students, I have worked to develop ways to bring mathematics to a wider audience in interesting and understandable ways.
- Math 210: Ordinary Differential Equations