Modern theory of dynamical systems

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Department of Fundamental Mathematics (Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod))

Course type:

Compulsory course

When:

1 year, 1, 2 module

Instructors

Barinova, Marina

Shubin, Danila

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

Assessment Elements

• Exam
• Workshop activities

Interim Assessment

• 2024/2025 2nd module
  0.5 * Exam + 0.5 * Workshop activities

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

Authors

• Barinova Marina Konstantinovna