2024/2025

Systems with regular dynamics

Type: Mago-Lego

Delivered by: Department of Fundamental Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Elena Gurevich

Language: English

ECTS credits: 6

Contact hours: 56

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

Expected Learning Outcomes

• owns the terminology and basic facts of the section

Course Contents

• Topology of manifolds and vector fields on manifolds.
• Local analysis
• Hyperbolic dynamics.
• Morse-Smale Systems

Assessment Elements

• контрольная работа
• доклад

Interim Assessment

• 2024/2025 2nd module
  0.3 * доклад + 0.4 * доклад + 0.3 * контрольная работа

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

Authors

• GUREVICH ELENA YAKOVLEVNA