Introduction to Dynamical Systems and Chaos

Instructor:  Dr. Imre Péter Tóth

Text: Kathleen T. Alligood, Tim D. Sauer, James A. Yorke: Chaos -- An Introduction to Dynamical Systems; Springer, 1996

Prerequisite:  things you will need to know: calculus (limits, differentiation, differentiation of functions in several variables, continuity, open/closed sets) and linear algebra (Euclidean space, matrix of a linear mapping, eigenvalues, eigenvectors of a linear mapping; canonical form,)

• one-dimensional and two-dimensional maps as dynamical systems
• limit sets and recurrence
• chaos and Lyapunov exponents
• symbolic dynamics, Smale horseshoe
• fractals and fractal (box counting) dimension
• differential equations as dynamical systems; limit sets and recurrence
• Lorenz attractor
• bifurcations

I intend to illustrate the material with as many examples of applications as possible. Those who are interested can have exercises requiring computer simulation both for homework and midterm.