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Course Syllabus

Master 2023/2024

Systems with regular dynamics

Category 'Best Course for Career Development'
Type: Elective course (Mathematics)
Area of studies: Mathematics
Delivered by: Department of Fundamental Mathematics
Where: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)
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
Contact hours: 52

Course Syllabus

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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

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

Expected Learning Outcomes

  • owns the terminology and basic facts of the section
Course Contents

Course Contents

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

Assessment Elements

  • non-blocking экзамен
  • non-blocking контрольная работа
Interim Assessment

Interim Assessment

  • 2023/2024 2nd module
    0.2 * контрольная работа + 0.2 * контрольная работа + 0.6 * экзамен
Bibliography

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 Iakovlevna