F6180 Introduction to nonlinear dynamics

Faculty of Science
Autumn 2001
Extent and Intensity
2/1/0. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Celý, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Prerequisites (in Czech)
Základy teoretické mechaniky a obyčejných diferenciálních rovnic.
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
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 8020004165. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. Masaryk University. ISBN 80-210-1130-0. 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
Assessment methods (in Czech)
Přednáška a individuální cvičení na PC.
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.
General note: Předpokládá znalosti ze základních kurzů M a F.
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 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2001, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2001/F6180