| Unit name | Dynamical Systems and Ergodic Theory 4 |
|---|---|
| Unit code | MATHM6206 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Ulcigrai |
| Open unit status | Not open |
| Pre-requisites |
Analysis 1 (MATH11006) and Calculus 1 (MATH 11007), or equivalent units |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Dynamical Systems is an active field in pure and applied mathematics that involves analysis, geometry and number theory. Dynamical systems can be obtained iterating a function or evolving in time the solution of an equation, and often display chaotic long term behaviour. Branches of ergodic theory provide tools to quantify and predict this chaotic behaviour on average. The emphasis in the first part of the unit will be on presenting many fundamental examples of dynamical systems, e.g. rotations, the Baker map, continued fractions. Driven by the examples, it will motivate and introduce key phenomena and concepts. The second part of the unit will formalize the basic definitions and present fundamental theorems and results in topological dynamics, in symbolic dynamics and in particular in ergodic theory. Proofs the main theorems will be given. Finally the unit will address applications both to other areas of mathematics, such as number theory, and to concrete problems such as data storage and Internet search.
