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Regular version of the site

# Applied theory of dynamical systems

2022/2023
ENG
Instruction in English
4
ECTS credits

Turaev, Dmitry

### Course Syllabus

#### Abstract

The course is designed as an introduction to the applied aspects of the modern theory of dynamical systems. A rigorous presentation of the theory of global bifurcations in multidimensional systems and its application to problems of biology will be given. The fundamentals of the dynamics of partial differential equations and the theory of dynamical systems under the action of random perturbations 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

• Control work
• exam

#### Interim Assessment

• 2022/2023 2nd module
0.7 * exam + 0.3 * Control work

#### 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.