Autonomous differential equations and dynamical systems. Linear systems, canonic forms, phase portraits, stability, topological equivalence. Nonlinear systems: Hyperbolic and non-hyperbolic critical points. Linearization, Stability, Bifurcations, Central manifolds. Limit sets and attractors. Periodic orbits, limit cycles. Bifurcations. Poincare mapping. The Poincare-Bendixon Theorem. Homoclinic and heteroclinic points, chaos. The Sharkovskii Theorem, the Melnikoff function, shadowing lemma.
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Aktuální odborné články v mezinárodních matematických časopisech.
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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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Katok, A., Hasselblatt, B. (1995). Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, Cambridge.
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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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Steven H. Strogatz. (2014). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Boca Raton.
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