MATE5411 Symbolic Dynamics (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Grading scale:
0-5
Description
The course introduces fundamental concepts of topological and symbolic dynamical systems as group or monoid actions, such as homomorphisms and factor maps, orbit closures and subsystems, mixing properties, recurrence properties and sensitivity to initial conditions. In symbolic systems the course introduces the concepts of shift spaces, subshifts of finite type, sofic and effective subshifts and sliding block codes. The course also teaches basic facts of the compact metric spaces and the Cantor topology on shift spaces.
Learning outcomes
To learn the main concepts of topological dynamical systems, symbolic dynamics and shift spaces. To be able to use topology as a tool in the context of symbolic dynamics.
Additional information
Course will be given every other spring (in odd years).