MU:MU03050 Dynamical Systems I - Course Information
MU03050 Dynamical Systems I
Mathematical Institute in OpavaWinter 2018
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: z (credit).
- Guaranteed by
- doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava - Course Enrolment Limitations
- The course is offered to students of any study field.
- Course objectives
- This course is a graduate level introduction to the mathematical theory of discrete dynamical systems on compact metric spaces and additionaly on the intercal. We will discuss some fundamental examples in the field, including circle rotations, shifts and subshifts, quadratic maps. We cover topics such as limit sets and recurrence, topological mixing, transitivity, entropy and symbolic dynamics.
- Syllabus
- 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.
- 1. Elementary notions - orbit (full, forward, backward), fixed point, eventually fixed point, phase portrait, Brower fixed
- Literature
- recommended literature
- L. S. Block, W. A. Coppel. Dynamics in one dimension. Lecture Notes in Mathematics, 1513. Springer-Ver, 1992. info
- R. L. Devaney. An introduction to chaotic dynamical systems. Second edition, 1989. info
- J. Smítal. On functions and functional equations. Adam Hilger, Ltd., Bristol, 1988. ISBN 0-85274-418-8. info
- P. Walters. An introduction to ergodic theory. Graduate Texts in Mathematics, 79. Springer-Verl, 1982. info
- H.Furstenberg. Recurrence in Ergodic Theory and Combinational Number Theory. Princeton University Press, Princeton, New Jersy, 1981. 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
- Credid: credit test
Final exam: final test and oral exam
- Enrolment Statistics (Winter 2018, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2018/MU03050