Chaotic Dynamical Systems
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.
Schedule on datanose
- Course manual:
Course manual. The course manual will be regularly updated to reflect the current version of the planning.
- Test October 27:
The test on October 27 is a two hour test, from 9-11 o'clock, on covered material from Sections 1.1-1.12 in Devaney.
An example test.
The test with solutions.
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 20 minutes
(a precise schedule will be determined later).