Math 558 - Applied Dynamical Systems - Winter 1999


Instructor: Robert Krasny, 2842 East Hall, 763-3505,

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.

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

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

linear algebra, differential equations

Course Requirements:
homework assignments, final exam/project