| Type: | Ph.D.-level, Open University
Language: English |
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Previous course: C1751
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No credit points with: C1751
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Prerequisite: 10231/01248/04211
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Recommended semester: 7th - 9th semester
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Scope and form: Lectures, seminars and homework assignments
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Examination: Evaluation of compulsory reports. (13-scale)
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Participant limitation: max. 40
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Department: Department of Physics
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Aim: To present an advanced treatment of some of the main elements of modern chaos theory.
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Contents: Examples of chaos in physical and technical systems. Attractors and their basins of attraction. Stable and unstable manifolds. Bifurcation theory. Continuation methods. One- and two-dimensional iterated mappings. The horseshoe mapping. Routes to chaos. Feigenbaum's universal theory. Sarkowskii's theorem. Homoclinic orbits. Frequency locking. Torus destabilisation. Intermittency. Crises. Symbolic dynamics. Renormalisation theory. Fractals and multifractals. Lyapunov exponents. Fractal basin boundaries between coexisting solutions. Coupled period-doubling systems. Chaos synchronization and control of chaos. Chaotic scattering. Chaos in conservative and nearly conservative systems. Quantum chaos.
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