Math 558 - Applied Dynamical Systems - Winter 1999

Q&A

Instructor: Robert Krasny, 2842 East Hall, 763-3505, krasny@umich.edu

Time and Location: TuTh, 8:30-10am, 3096 East Hall

The theory of dynamical systems provides a means for understanding complex behaviour in a broad range of applications. This course is an introduction to the theory, with emphasis on chaotic dynamics. We will study continuous systems (differential equations) and discrete systems (iterated maps). I aim to provide a broad overview of the subject as well as an in-depth analysis of specific examples. The course is intended for students in mathematics, engineering, and science.

The topics include: bifurcations (transcritical, pitchfork, subcritical, supercritical, Hopf), stable and unstable manifolds, dissipative systems, attractors, logistic map, period-doubling, Feigenbaum sequence, renormalization, chaos, Lyapunov exponent, fractals, Cantor set, Hausdorff dimension, Lorenz system, nonlinear oscillations, quasiperiodicity, Hamiltonian systems, integrability, resonance, KAM tori, homoclinic intersections, Melnikov's method.

Text:
Nonlinear Systems by P. G. Drazin, Cambridge University Press

References:
Chaos in Dynamical Systems by Edward Ott, Cambridge University Press
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer and Philip Holmes, Springer-Verlag

Prerequisites:
linear algebra, differential equations

Course Requirements:
homework assignments, final exam/project