PřF:F6180 Introd. to nonlinear dynamics - Course Information
F6180 Introduction to nonlinear dynamics
Faculty of ScienceAutumn 2011 - acreditation
The information about the term Autumn 2011 - acreditation is not made public
- Extent and Intensity
- 2/1/0. 2 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor) - Guaranteed by
- prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc. - Prerequisites
- F5030 Intro. to Quantum Mechananics
Basic knowledge from introductory courses of mathematics, physics, theoretical mechanics and ordinary differential equations. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- This lecture is introductory course of nonlinear dynamics dealing with solution of some simple classical systems with added nonlinear terms and deterministic chaos.
After passing this course the students should be able to
- list and explain basic methods of solving classical systems
- apply these methods in case of Hamiltonian systems with nonlinear terms
- define and also identify a problem, leading to deterministic chaos. - Syllabus
- 1)Dynamical systems with discrete and continuous time evolution. Autonomous equations. State space, flow in phase space, fixed points, phase portraits,classification of linear systems, application to nonlinear systems.
- 2)Some one-dimensional nonlinear systems (Duffing oscillator, mathematical pendulum,forced oscillator).
- 3)Hamiltonian systems: integrability, invariants, periodic solutions, invariant tori and deterministic chaos, KAM theorem. Toda lattice,Hénon-Heiles potential, convex billiards.
- 4)One-dimensional maps: logistic equation, bifurcations, period-doubling , Feigenbaum theory.
- 5)Dissipative systems: time evolution in phase space, divergence theorem, Lyapunov exponents, strange attractors (Hénon, Lorenz, Rösler),fractal dimension.
- Literature
- HORÁK, Jiří and Ladislav KRLÍN. Deterministický chaos a matematické modely turbulence. 1. vyd. Praha: Academia, 1996, 444 s. ISBN 8020004165. info
- KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
- HILBORN, Robert C. Chaos and nonlinear dynamics : an introduction for scientists and engineers. New York: Oxford University Press, 1994, 654 s. ISBN 0195088166. info
- LICHTENBERG, Allan J. and M. A. LIEBERMAN. Reguljarnaja i stochastičeskaja dinamika. New York: Springer-Verlag, 1983, 499 s. ISBN 0387907076. info
- Teaching methods
- Lecture + individual work on PC
- Assessment methods
- Demands for colloquium: oral testing of the knowledge gained, based on the individual work during the semester presentation.
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Information on course enrolment limitations: F5030 - Teacher's information
- http://monoceros.physics.muni.cz/~jancely
- Enrolment Statistics (Autumn 2011 - acreditation, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2011-acreditation/F6180