MATH 717: Applied Dynamical Systems (spring 2008)

Instructor: John Guckenheimer

Meeting Time & Room

Nonlinear dynamical systems are used as models in every field of science and engineering. Universal patterns of behavior, including "chaos," have been observed in large sets of examples. Mathematical theories describing geometrically the qualitative behavior of "generic" systems explain many of these patterns.

The core of this course is an introduction to bifurcation theory for dynamical systems. Specific systems arising in examples will be used as case studies to illustrate concepts and to demonstrate analytic methods in concrete settings. More advanced topics that will be discussed include:

• numerical methods for computing periodic orbits and bifurcations,
• dynamical systems with multiple time scales,
• bifurcation in symmetric systems.

Some experience with dynamical systems theory will be helpful, but material from the graduate dynamics courses MATH 617/618 will not be assumed. Grades will be based upon biweekly homework assignments and a course project.