MATA310 Introduction to Dynamical Systems (4 cr)
Basics of discrete dynamical systems. Examples: circle rotations, linear expansive maps of the circle, billiards. Topological properties of dynamical systems, transitivity, mixing, chaos.
The course introduces the basics of discrete dynamical systems and illustrates theory-related concepts through the behavior of exemplary systems. After completing the course the student
- knows what discrete dynamical system means
- knows how to solve basic properties in simple systems
- understands the basics of graphical analysis of dynamical systems and how to apply it
- knows the dynamical properties of basic examples and is able to deduce them
- knows the topological concepts concepts related to dynamical systems and is able to examine those of simple systems
- knows the basics of symbolic dynamics and its application in examining other dynamical systems
Description of prerequisites
Introduction to mathematical analysis 1-4, Linear algebra and geometry 1, Vector calculus 1.
Vector calculus 2 and Linear algebra and geometry 2 are also recommended.
- Katok, Hasselblatt: Introduction to the Modern Theory of Dynamical Systems.; ISBN: 978-0521575577
- Hirsch, Smale, Devaney: Differential Equations, Dynamical Systems, and an Introduction to Chaos; ISBN: 978-0123820105
Teaching (4 cr)
28h luentoja, 7 harjoituskertaa.
Exam (4 cr)