MATH 618: Smooth Ergodic Theory (Spring 2005)

Instructor: John Guckenheimer

Meeting Time & Room

This course is about chaos and strange attractors in dynamical systems. Smooth ergodic theory looks at statistical aspects of these phenomena. Mathematical concepts of invariant measures, entropy, Hausdorff dimension and Liapunov exponents will be defined and studied. The theory will be examined in the simplest setting of hyperbolic attractors. If time permits, larger classes of systems will also be studied.

New techniques of data analysis, called nonlinear times series analysis, have been developed using the concepts of smooth ergodic theory. This course will present case studies and discuss the computational issues involved in nonlinear times series analysis.

Students in the course will be expected to do a course project and to present some of the material in course lectures. Students interested in analyses of real data are particularly welcome.

Last modified: October 1, 2004