Master
2024/2025
Systems with regular dynamics
Type:
Elective course (Mathematics)
Area of studies:
Mathematics
Delivered by:
Department of Fundamental Mathematics
When:
2 year, 1, 2 module
Mode of studies:
offline
Open to:
students of all HSE University campuses
Instructors:
Elena Gurevich
Master’s programme:
Mathematics
Language:
English
ECTS credits:
6
Course Syllabus
Abstract
The course is intended for masters of the second year of study. It is aimed at studying qualitative theory of systems with regular dynamics.
Learning Objectives
- The aim of the course is to give introduction to classical and modern problems of the qualitative theory of systems with regular dynamics
Course Contents
- Topology of manifolds and vector fields on manifolds.
- Local analysis
- Hyperbolic dynamics.
- Morse-Smale Systems
Bibliography
Recommended Core Bibliography
- • R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin/Cum-. (2015). Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.20873EF4
- 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.
- 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
- Геометрическая теория динамических систем : введение : вводные курсы, Палис, Ж., 1986
Recommended Additional Bibliography
- Introduction to the Modern Theory of Dynamical Systems, With a supplement by Anatole Katok and Leonardo Mendoza, XVIII, 802 p., Katok, A., Hasselblatt, B., 1996