F6180 Introduction to nonlinear dynamics

Faculty of Science
Autumn 2006
Extent and Intensity
2/1/0. 2 credit(s). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Supervisor
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Timetable
Tue 7:00–7:50 Fs1,01017, Tue 8:00–9:50 Fs1,01017
Prerequisites (in Czech)
F5030 Intro. to Quantum Mechananics
Pedpokládá znalosti ze základních kurzů M a F, základy teoretické mechaniky a obyčejných diferenciálních rovnic.
Course Enrollment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
Fields of study the course is directly associated with
Course objectives
Introductory course of nonlinear dynamics. Dynamical systems with discrete and continuous time evolution. Autonomous equations. State space, flow in phase space, fixed points, phase portraits,classification of linear systems. Some one-dimensional nonlinear systems. Hamiltonian systems: integrability, invariants, periodic solutions, invariant tori and deterministic chaos, KAM theorem. One-dimensional iterative maps: logistic equation, bifurcations, period-doubling , Feigenbaum theory. Dissipative systems: time evolution in phase space, strange atractors, Lyapunov exponents, fractal dimension.
Literature
  • HORÁK, Jiří and Ladislav KRLÍN. Deterministický chaos a matematické modely turbulence. 1. vyd. Praha: Academia, 1996. 444 s. ISBN 80-200-0416-5. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995. 207 s. ISBN 80-210-1130-0. info
  • HILBORN, Robert C. Chaos and nonlinear dynamics :an introduction for scientists and engineers. 1st ed. Oxford: Oxford University Press, 1994. x, 654 s. ISBN 0-19-508816-6. info
  • LICHTENBERG, Allan J. and Michael A. LIEBERMAN. Reguljarnaja i stochastičeskaja dinamika. New York: Springer-Verlag, 1983. 499 s. ISBN 0-387-90707-6. info
Assessment methods (in Czech)
Přednáška a individuální cvičení na PC.
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Information on course enrollment limitations: F5030
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, autumn 2012, autumn 2013.
  • Enrollment Statistics (Autumn 2006, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2006/F6180

Other references: 

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