MU14642 Introduction to Catastrophe and Chaos Theory

Mathematical Institute in Opava
Winter 2022
Extent and Intensity
1/0/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA ( B )
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
The students obtain some basic knowledges about discrete dynamical systems and catastrophe theory.
Syllabus
  • - 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
Literature
    recommended literature
  • J. Smítal. O funkciách a funkcionálnych rovniciach. info
  • Y. Chen, A. Y. T. Leung. Bifurcation and chaos in engineering. Springer Verlag, 1998. ISBN 3-540-76242-6. info
  • Arnoľd V. I. Teoria katastrof. Alfa Bratislava, 1986. info
  • R. Gilmore. Catastrophe theory for scientists and engineers. John Wiley and Sons, 1981. info
  • T. Poston, I. Stewart. Catastrophe theory and its applications. Pitman London, 1978. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Writing solution of three examples.
The course is also listed under the following terms Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (recent)
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