MU03051 Dynamical Systems II

Mathematical Institute in Opava
Summer 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Mgr. Samuel Joshua Roth, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava
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
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.
  • 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.
    required literature
  • D. K. Arrowsmith, C. M. Place. An introduction to Dynamical Systems. Cambridge University Press, 1990. info
    recommended literature
  • L. Barreira, C. Valls. Dynamical systems : an introduction. Springer-Verlag London, 2013. ISBN 978-1-4471-4834-0. info
  • S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag New York, 2003. ISBN 978-0-387-00177-7. info
Language of instruction
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Course credit: ability to verify notion on given examples
Final exam: knowledge of basic notions and assertions, at least partial understanding of theory
The course is also listed under the following terms Winter 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2021.
  • Enrolment Statistics (Summer 2022, recent)
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