MU:MU03051 Dynamical Systems II - Course Information
MU03051 Dynamical Systems II
Mathematical Institute in OpavaSummer 2024
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Jana Hantáková, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Jana Hantáková, Ph.D.
Mathematical Institute in Opava - Timetable
- Wed 9:45–11:20 117
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- ( MU03049 Dynamical Systems I || MU03050 Dynamical Systems I ) && TYP_STUDIA(BN)
- 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)
- Geometry and Global Analysis (programme MU, N1101)
- Mathematical Analysis (programme MU, NMgr-M)
- Mathematical Analysis (programme MU, N1101)
- Mathematical Methods in Economics (programme MU, B1101)
- Course objectives
- This course is a graduate level introduction to the mathematical theory of continuous dynamical systems on manifolds. We will discuss some fundamental examples in the field and bifurcations.
- Syllabus
- 1. Flow - flow, trajectory, equilibria.
2. Invariant sets - alpha nad omega limit set of the folw, closed orbit, Poincaré - Bendixson Theorem.
3. Bifurcation I. - bifurcation, bifurcation diagram.
4. Examples - pitchfork, transcritical, saddle node and Poincaré - Andronov - Hopf bifurcation.
5. Bifurcation II. - qualitative equivalence of the linear systems, hyperbolic systems, bifurcation of linear systems.
6. Bifurcation III. - Hartman - Grobman and Poincaré - Andronov - Hopf theorems. Examples of nonhyperbolic equilibria, supercritical bifurcation.
7. Centram manifold - central manifolds and their applications.
- 1. Flow - flow, trajectory, equilibria.
- Literature
- required literature
- D. K. Arrowsmith, C. M. Place. An introduction to Dynamical Systems. Cambridge University Press, 1990. 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
- Course credit: solving at least ten problems assigned during the semester and a subsequent presentation ability to verify notion on given examples
Final exam: knowledge of basic notions and assertions, at least partial understanding of theory
- Enrolment Statistics (recent)
- Permalink: https://is.slu.cz/course/sumu/summer2024/MU03051