Official description

The theory of nonlinear dynamical systems with applications to many areas of physics. Topics include stability, bifurcations, chaos, universality, maps, strange attractors and fractals. Geometric, analytical and computational methods will be developed.

Additional information

A course on topics in nonlinear physics. Finite dimensional flows, bifurcations, instabilities and relation to phase transitions. Index theory and its use for the classification of topological defects. Chaos, strange attractors, maps and fractals. An introduction to the renormalization group applied to the Feigenbaum sequence and the period-doubling route to turbulence. Examples from nonlinear classical and quantum (few- or many-body) physics, chemistry, biology, and sociology will be given to illustrate the nonlinear phenomena studied. Computer exercises will be used throughout the course.