Deterministic Chaos

Part 1 Experiments and simple methods: experimental detection of deterministic chaos; the periodically kicked rotator. Part 2 Piecewise linear maps and deterministic chaos: the Bernoulli shift; characterization of chaotic motion; deterministic diffusion. Part 3 Universal behaviour of quadratic maps: parameter dependence of the iterates; pitchfork bifurcations and the doubling transformation; self-similarity, universal power spectrum and the influence of external noise; behaviour of the logistic map for "r-alpha is less than or equal to r"; parallels between period doubling and phase transitions; experimental support for the bifurcation route. Part 4 The intermittency route to chaos: mechanisms for intermittency; renormalization-group treatment of intermittency; intermittency and l/f-Noise; experimental observation of the intermittency route. Part 5 Strange attractors in dissipative dynamical systems: introduction and definition of strange attractors; the Kolmogorov entropy; characterization of the attractor by a measured signal; pictures of strange attractors and fractal boundaries. Part 6 The transition from quasiperiodicity to chaos: strange attractors and the onset of turbulence; universal properties of the transition from quasiperiodicity to chaos; experiments and circle maps; routes to chaos. Part 7 Regular and irregular motion in conservative systems: coexistence of regular and irregular motion; strongly irregular motion and ergodicity. Part 8 Chaos in quantum systems?: the quantum cat map; a quantum particle in a stadium; the kicked quantum rotator. Part 9 Controlling chaos: stabilization of unstable orbits; parametric resonance from unstable periodic orbits.