Course: Dynamical Systems I

» List of faculties » MU » MU
Course title Dynamical Systems I
Course code MU/03050
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
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
  • MÁLEK Michal, doc. RNDr. Ph.D.
Course content
1. Elementary notions - orbit (full, forward, backward), fixed point, eventually fixed point, phase portrait, Brower fixed theorem, Sharkovskii ordering. 2. Hyperbolicity - critical point, hyperbolic point, attractive and repulsice point. 3. Quadratic system - logistic map, the tent map, rotations of the circle. 4. Symbolical dynamics - shift space and shift map. 5. Topological dynamics I. - minimal sets, limit sets, nonwandering sets, conjugacy. 6. Topological dynamics II. - transitivity, total transitivity, mixings, their relations and relations to the dense orbit. 7. Topological dynamics III. - recurrence and relations to ninimality. 8. Topological dynamics IV. - topological entropy.

Learning activities and teaching methods
Recommended literature
  • H.Furstenberg. Recurrence in Ergodic Theory and Combinational Number Theory. Princeton University Press, Princeton, New Jersy, 1981.
  • J. Smítal. On functions and functional equations. Adam Hilger, Ltd., Bristol, 1988. ISBN 0-85274-418-8.
  • L. S. Block, W. A. Coppel. Dynamics in one dimension. Lecture Notes in Mathematics, 1513. Springer-Verlag, Berlin, 1992.
  • P. Walters. An introduction to ergodic theory. Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982.
  • R. L. Devaney. An introduction to chaotic dynamical systems. Second edition, 1989.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Winter