Course: Dynamical Systems 3

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Course title Dynamical Systems 3
Course code KMA/DS3
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Fišer Jiří, RNDr. Ph.D.
  • Andres Jan, prof. RNDr. dr hab. DSc.
Course content
1.Iterated function systems, fractals and fractal dimension 1. Introduction to the subject. Examples of fractals. 2.Iterated function systems, fractals and fractal dimension 2. Prehistory of fractal geometry, Hausdorff and box-counting dimensions. 3.Iterated function systems, fractals and fractal dimension 3. Iterated function systems (IFS), self-similarity dimension, Moran formula. 4.Chaotic dynamics on fractals 1. Hyperspaces, Hausdorff metric, address points, code space. 5.Chaotic dynamics on fractals 2. Transformation from code spaces into fractals, metrics on code space. 6.Chaotic dynamics on fractals 3. Totally disconnected IFS, just-touching IFS, periodic point of IFS. 7.Chaotic dynamics on fractals 4. Discrete and continuous dynamical systems, dynamics on fractals. 8.Homoclinic points, chaos and strange attractors 1. Hyperbolic sets, orbits, pseudo-orbits, shadowing lemma. 9.Homoclinic points, chaos and strange attractors 2. Homoclinic points, transversal homoclinic points, chaotic map. 10.Sharkovskij and Li-York theorems. Sharkovskij and Li-York theorems and their application to tent maps. 11.Logistic equation and bifurcations 1. Study of logistic (difference) equation, Feigenbaum constant. 12.Logistic equation and bifurcations 2. Analysis of the Verhulst model, bifurcation diagrams

Learning activities and teaching methods
  • Attendace - 39 hours per semester
  • Semestral Work - 50 hours per semester
  • Homework for Teaching - 30 hours per semester
Learning outcomes
To introduce the basic results and principles of the theory of chaos and fractals.
Comprehension To uderstand the basic principles of the theory of chaos and fractals.
Knowledge of differential and integral calculus and basic information from the theory of ordinary differential equations to the extent of the course KMA/ODR1.

Assessment methods and criteria
Oral exam

Credit: the student has to write a course work.
Recommended literature
  • K. J. Palmer. Bifurcations, chaos and fractals (článek).
  • M. F. Barnsley. (1993). Fractals everywhere. Boston, MA: Academic Press Professional. xiv.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 2 Winter