MU24011 Continuous Dynamical Systems

Mathematical Institute in Opava
Summer 2017
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Michal Málek, 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
Syllabus
  • 1. Flow - flow, trajectories, stationary points.
    2. Invariant sets - alpha (omega) limit points of trajectories, alpha (omega) limit points of a flow. Closed orbits. Poincare-Bendixson theorem.
    3. Bifurcations I - bifurcation value, diagram.
    4. Examples of bifurcations - pitchfork, transcritical, saddle - knot, Poincare-Andronov-Hopf.
    5. Bifurcations II - qualitative equivalence of linear systems, hyperbolic systems, bifurcations of linear systems.
    6. Bifurcations III - Hartman-Grobman and Poincare-Andronov-Hopf theorems, examples of nonhyperbolic fixed points. Supracritical bifurcations.
    7. Central variety - central variety, pendulum with exterior force.
    8. Examples of global bifurcations - homoclinic bifurcations, period doubling.
Literature
    recommended literature
  • J. Hale, H. Kocak. Dynamics and bifurcations. Springer Verlag, 1991. info
  • 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.
The course is also listed under the following terms Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2017, recent)
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