Applied theory of dynamical systems

2025/2026

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Кафедра фундаментальной математики (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:

Курс обязательный

Когда читается:

4-й курс, 3 модуль

Преподаватель

Шемахин Александр Юрьевич

Course Syllabus

Abstract

The course is designed as an introduction to the applied aspects of the modern theory of dynamical and quasidynamical systems. A rigorous presentation of the theory of numerical modelling in multidimensional systems and its application to problems of plasma systems will be given. The fundamentals of programming algorithms for solving such systems will be presented.

Learning Objectives

• Introduction to the theory of dynamical systems and introduction to some applications

Expected Learning Outcomes

• The learner will be able to: formulate the notion of a dynamical system, provide examples of first-order dynamics, reduce a stationary second-order differential equation to a first-order dynamical system, and analyze the resulting system for stability and phase trajectories.
• The learner will be able to analyze examples from electrodynamics, plasma physics, and chemical kinetics and formulate boundary value problems for calculating plasma parameters in outer space, as well as for plasma-chemical and chemical reactions in industrial reactors.
• The learner will be able to master the basics of developing and testing computational programs in C++, apply the studied numerical methods, and estimate the order of convergence and accuracy of the obtained solution
• The learner will be able to determine the structure of reporting presentations and explain the physical meaning of the calculation results.
• Able to formulate and correctly set tasks in the field of: Notion of a dynamical system, examples, first-order dynamics, Reducing a stationary equation of the second order to a dynamical system
• After studying the section, students will be able to analyze practical cases in electrodynamics and plasma physics, correctly formulate boundary value problems for calculating plasma parameters in outer space and industrial reactors, and apply equations of plasma-chemical and chemical reactions to model processes in real-world technological and astrophysical environments.

Course Contents

• Elementary dynamics.
• Practical cases
• Numerical methods
• The calculation code writing
• Results presentation

Assessment Elements

• Лабораторная работа 1
• Экзамен

Interim Assessment

• 2025/2026 3rd module
  0.5 * Лабораторная работа 1 + 0.5 * Экзамен

Bibliography

Recommended Core Bibliography

• Differentiable Dynamical Systems : An Introduction to Structural Stability and Hyperbolicity, XI, 192 p., Wen, L., 2016
• Dynamical Systems : Stability, Symbolic Dynamics, and Chaos, 2nd ed., 504 p., Robinson, C., 1999
• 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

Recommended Additional 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

Authors

• Shemakhin Aleksandr Iurevich
• Nozdrinova Elena Viacheslavovna