ETFNPV0003 Deterministic chaos

Institute of physics in Opava
winter 2023
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Martin Kološ, Ph.D. (lecturer)
RNDr. Martin Kološ, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Martin Kološ, Ph.D.
Institute of physics in Opava
Prerequisites (in Czech)
( FAKULTA ( FU )&& SOUHLAS )
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The subject acquaints students with behaviour of nonlinear systems including basic astrophysical applications.
Learning outcomes
Upon successful completion of the course, the student will:
- be able formulation of physical problems associated with deterministic chaos
- be able to use Wolfram Mathematica program for deterministic chaos problems solution for routine mathematical
- be able to analyze stability of bound physical systems
Syllabus
  • Basic topics of the subject
    - Dynamical systems - history and motivation
    - Programming tool Wolfram Mathematica
    - Sequence, logistic map, bifurcation
    - Fractals and their dimmension
    - Diferential equations, phase space,
    - Numerical solutions, function NDSolve
    - Hamilton formalis, motion in effective potential
    - Oscillators, Harmonic analysis
    - Poincare sections, rekurent plots, Lyapunov exponent
    - Three body problem, small perturbation
    - KAM theorem
    - Stability of Solar system
    - Temporal series analysis.
Literature
    recommended literature
  • Horák, J. Krlín, L. Deterministický chaos a podivná kinetika, Academia, 2007
  • Ott, E. Chaos in Dynamical Systems, Cambridge University Press, 1993
  • Tél, T., Gruiz, M. Chaotic Dynamics An Introduction Based on Classical Mechanics, Cambridge University Press, 2006
  • Koberlein, B., Meisel, D. Astrophysics through Computation: With Mathematica Support, Cambridge University Press, 2013
Teaching methods
Lecure and discussion. Excercises.
Assessment methods
oral exam, written test
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Information on course enrolment limitations: Erasmus
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fu/winter2023/ETFNPV0003