Бакалавриат
2024/2025
Прикладная теория динамических систем
Статус:
Курс обязательный (Математика)
Направление:
01.03.01. Математика
Кто читает:
Кафедра фундаментальной математики
Когда читается:
4-й курс, 3 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Шемахин Александр Юрьевич
Язык:
английский
Кредиты:
6
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
- Know the basic definitions of dynamics systems
- know the main results and examples
- be able to solve problems on the topic
Course Contents
- Elementary dynamics
- Periodic forcing and quasiperiodic dynamics
- Two-dimensional dynamics
- Synchronization theory
- Chaos
- Saddles and homoclinic structures
- Measure and dimensions
- Logistic map
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
- Hasselblatt, B., Takens, F., & Broer, H. W. (2010). Handbook of Dynamical Systems. Amsterdam: North Holland. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=344991
- 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
- Strogatz, S. H. (2000). Nonlinear Dynamics and Chaos : With Applications to Physics, Biology, Chemistry, and Engineering (Vol. 1st pbk. print). Cambridge, MA: Westview Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421098
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
- M. I. Freidlin, & A. D. Wentzell. (2012). Random Perturbations of Dynamical Systems (Vol. 1984). Springer.