I received a Ph.D. from University of California at Berkeley, in Physics, 1980. From 1980-1989 I was at the Institute for Fusion Studies, at the University of Texas. In 1989 I moved to Boulder, becoming Professor of Applied Mathematics.
Department of Applied Mathematics
University of Colorado at Boulder
Boulder, CO 80309-0526
(303) 492-4668 (secretary)
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.
Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts-flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics.
This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus.
I retired from being an editor of Physica D as of Dec 31, 1999. Please submit your papers to one of the current editors.
I retired as associate editor for the SIAM Journal on Applied Dynamical Systems on Dec 31, 2009.
I organized the 1995 SIAM Dynamical Systems Meeting in Snowbird Utah. The next meeting will be in Snowbird in May 2013. Stay in touch with the SIAG at DynamicalSystems.org. There you will find a the Dynamics online magazine, an image gallery, etc.
revised Jan 2014