Course: Dynamical Systems 3

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Course title Dynamical Systems 3
Course code KMA/DS3N
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
Lecturer(s)
  • Andres Jan, prof. RNDr. dr hab. DSc.
Course content
1. Iterated function systems. 2. Fractals as attractors of iterated function systems. 3. Fractal dimensions. 4. Deterministic chaos. 5. Numerics of chaotic trajectories - The Shadowing Lemma. 6. Transversal homoclinic points and the Melnikov function.

Learning activities and teaching methods
Lecture
  • 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.
Prerequisites
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 Applied Mathematics (2014) Mathematics courses 2 Winter