MU:MU03051 Dynamical Systems II - Course Information

MU03051 Dynamical Systems II

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Marek Lampart (lecturer)
RNDr. Marek Lampart (seminar tutor)

Guaranteed by

RNDr. Marek Lampart
Mathematical Institute in Opava

Prerequisites (in Czech)

MU03049 Dynamical Systems I || MU03050 Dynamical Systems I

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)
• Applied Mathematics in Risk Management (programme MU, B1102)
• Geometry (programme MU, M1101)
• Geometry (programme MU, N1101)
• Mathematical Analysis (programme MU, M1101)
• Mathematical Analysis (programme MU, N1101)
• Mathematical Methods in Economics (programme MU, B1101)
• Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
• Secondary School Teacher Training in Mathematics (programme FPF, M7504)
• Upper Secondary School Teacher Training in Mathematics (programme MU, N1101)
• Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)

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.

Literature

recommended 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)

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 (Summer 2011, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2011/MU03051