Course: Introduction to Catastrophe and Chaos Theory

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Course title Introduction to Catastrophe and Chaos Theory
Course code MU/14642
Organizational form of instruction Lecture
Level of course Bachelor
Year of study 2
Semester Winter
Number of ECTS credits 2
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
Course availability The course is available to visiting students
  • ŠTEFÁNKOVÁ Marta, doc. RNDr. Ph.D.
Course content
- nonlinear difference equations and discrete dynamical systems - fixed points of continuous function defined on an interval and their stability - cycles and their stability - bifurcation values of a parameter, Sharkovsky theorem - chaos origin, characterization of chaos - Feigenbaum constant - critical points of smooth maps - Hadamard lemma, inverse map theorem, Morse lemma - structural stability of smooth maps and systems of maps -Thom theorem and examples of the cusp catastrophe

Learning activities and teaching methods
Recommended literature
  • Arnoľd V. I. Teoria katastrof. Alfa Bratislava, 1986.
  • J. Smítal. O funkciách a funkcionálnych rovniciach.
  • R. Gilmore. Catastrophe theory for scientists and engineers. John Wiley and Sons, 1981.
  • T. Poston, I. Stewart. Catastrophe theory and its applications. Pitman London, 1978.
  • Y. Chen, A. Y. T. Leung. Bifurcation and chaos in engineering. Springer Verlag, 1998. ISBN 3-540-76242-6.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 2 Winter