MU:MU14642 Intr. to Catastrophe and Chaos - Course Information

MU14642 Introduction to Catastrophe and Chaos Theory

Extent and Intensity

1/0/0. 2 credit(s). Type of Completion: z (credit).

Teacher(s)

doc. RNDr. Kristína Smítalová, CSc. (lecturer)

Guaranteed by

doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava

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

• Applied Mathematics in Risk Management (programme MU, B1101)

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)

The course can also be completed outside the examination period.

Teacher's information

Writing solution of three examples.

• Enrolment Statistics (Winter 2012, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2012/MU14642