Master
2024/2025
Modern theory of dynamical systems
Type:
Compulsory course (Mathematics)
Area of studies:
Mathematics
Delivered by:
Department of Fundamental Mathematics
When:
1 year, 1, 2 module
Mode of studies:
offline
Open to:
students of one campus
Master’s programme:
Mathematics
Language:
English
ECTS credits:
6
Contact hours:
56
Course Syllabus
Abstract
The course is devoted to the description of the current state of the Theory of dynamic systems from the point of view of topological classification of important classes of systems with regular and chaotic dynamics.
Learning Objectives
- To show the current state of research in the field of discrete dynamical systems
- To introduce basic concepts of discrete dynamical systems
Expected Learning Outcomes
- The student reproduces basic definitions and statements given in the course
- The student explains the relationship between concepts and the roles of conditions in statements
- The student solves standard tasks, including proving simple statements
- The student proves non-trivial theorems
Course Contents
- Discrete dynamical systems and their invariant sets
- One-dimensional dynamics
- Diffeomorphisms on surfaces. Appearance of chaos.
- Multidimensional dynamics
Bibliography
Recommended Core Bibliography
- Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016
- Grines V., Medvedev Timur, Pochinka O. Dynamical Systems on 2- and 3-Manifolds. Switzerland : Springer, 2016.
Recommended Additional Bibliography
- Introduction to the modern theory of dynamical systems, Katok, A., 1999
- Katok, A. B., & Hasselblatt, B. (2002). Handbook of Dynamical Systems (Vol. 1st ed). Amsterdam: North Holland. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=207259