## 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,)

*Planned topics*
- 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.