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Lecturer(s)
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Andres Jan, prof. RNDr. dr hab. DSc.
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Rachůnková Irena, prof. RNDr. DrSc.
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Course content
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Autonomous differential equations and dynamical systems. Linear systems, canonic forms, phase portraits, stability, topological equivalence. Nonlinear systems -- local theory: Hyperbolic and non-hyperbolic critical points. Linearization, Stability, Bifurcations, Central manifolds. Nonlinear systems - global theory: Limit sets and attractors. Periodic orbits, limit cycles. Bifurcations. Poincare mapping. The Poincare-Bendixon Theorem. Homoclinic and heteroclinic points, chaos, the Melnikoff function, shadowing lemma, the Smale Horseshoe, the Sharkovskii Theorem
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Master essential tools of the theory of dynamical systems.
Comprehension Demonstrate a good orientation ín the theory of dynamical systems.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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C. Robinson. (1995). Dynamical Systems. CRC Press, Boca Raton.
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D.K. Arrowsmith, C.M. Place. (1991). An Introduction to Dynamical Systems. Cambridge Univ. Press, Cambridge.
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F. Verhulst. (1990). Nonlinear Differential Equations and Dynamical Systems. Springer-Verlag.
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H.O. Peitgen, H. Jurgens, D.Saupe. (1992). Chaos and Fractals. Springer, Berlin.
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J. Guckenheimar, P. Holmes. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, New York.
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J. Hale, H. Kocak. (1991). Dynamics and Bifurcations. Springer-Verlag, New York.
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J.H. Hubbart, B.H. West. Differential Equations: A Dynamical Systems Approach I, II. Springer-Verlag, New York, 1991, 1995.
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L.Perko. (1991). Differential Equations and Dynamical Systems. Springer-Verlag, New York.
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S.N. Chow, J.K. Hale. (1982). Methods of Bifurcation Theory. Springer, Berlin.
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