Chaotic Dynamical Systems

Content:
Modern dynamical systems theory originates with the work of Poincare, who revolutionized the study of dynamical systems by introducing qualitative techniques of geometry and topology to discuss global properties of solutions. The study of chaotic dynamical systems from the 1960s on lead to a breakthrough in science and an explosion of interest in the field of dynamical systems. This course investigates nonlinear dynamical systems and explains basic ideas of the field in low dimensional settings of iterated maps on the line and in the plane. Important results and ideas are explained in this context, such as symbolic dynamics, "period three implies chaos", period doubling route to chaos, the Smale horseshoe map and bifurcations of periodic points.

Course manual:
Course manual. The course manual will be regularly updated to reflect the current version of the planning.

Test October 26:
The test on October 26 is a two hour test, from 9-11 o'clock, on covered material from Chapter 1 in Devaney. The test with solutions.

Projects:
Projects. The projects are carried out in groups of two to four persons. Every group will write a short report (a few pages suffice) presenting a main mathematical statement and mathematical explanation thereof. In the last week groups present their work in presentations of around 15 minutes (a precise schedule will be determined later). Here is an example report from last year.

Test December 19:
The test on December 19 is a two hour test, from 9-11 o'clock, on the covered material from Devaney. The final test from last year. The final test from last year, with some answers.