F6180 Introduction to nonlinear dynamics

Faculty of Science
Autumn 2015
Extent and Intensity
2/1/0. 2 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Wed 15:00–16:50 F3,03015, Thu 18:00–18:50 F4,03017
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
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)
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Information on course enrolment limitations: F5030
Teacher's information
http://monoceros.physics.muni.cz/~jancely
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 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2015/F6180