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Lecturer(s)
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Andres Jan, prof. RNDr. dr hab. DSc.
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Course content
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1. Various definitions and examples of fractals. 2. Fractals as attractors of iterated function systems. 3. Fractal dimensions. 4. Deterministic chaos. 5. Numerics of chaotic trajectories - The Shadowing Lemma. 6. Models of chaotic behaviour.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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To understand the basic philosophy of chaotic dynamics (chaos vs. order) and fractal geometry (for which the Euclidean geometry is insufficient).
Knowledge The students will be familiar with basic results an principles in the theory of chaos and fractals.
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Prerequisites
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Knowledge of differential and integral calculus and basic information from the theory of ordinary differential equations.
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Assessment methods and criteria
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unspecified
Active participation on tutorials.
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Recommended literature
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Andres, J., Fišer, J., & Rypka, M. (2015). Dynamické systémy 3: úvod do teorie deterministického chaosu a fraktální geometrie.
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Barnsley, M. F. (1993). Fractals everywhere. 2nd ed.. London: Academic Press.
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Devaney, R. L. (2020). A First Course in Chaotic Dynamical Systems: Theory and Experiment. 2nd ed. Boca Raton: CRC Press.
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Falconer, K. J. (2014). Fractal geometry: mathematical foundations and applications. Third edition. Chichester, West Sussex: Wiley.
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Peitgen, H. O., Jürgens, H., & Saupe, D. (2004). Chaos and fractals: new frontiers of science. New York, N.Y: Springer.
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Robinson, C. (1999). Dynamical systems: stability, symbolic dynamics, and chaos. 2nd ed. Boca Raton: CRC Press. Studies in advanced mathematics.
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