Browse Hierarchy MTH6107: Chaos and Fractals

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The main aims are twofold: to illustrate (rigorously) how simple deterministic dynamical systems are capable of extremely complicated or chaotic behaviour; to make contact with real systems by considering a number of physically motivated examples and defining some of the tools employed to study chaotic systems in practice. Discrete and continuous dynamical systems, repellers and attractors, Cantor sets, symbolic dynamics, topological conjugacy for maps, definition of chaos. Fractals, iterated function systems, Julia sets.

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