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Resonance and fractal geometry

Resonance and fractal geometry

Summaryi. resonance in

Summaryi. resonance in parametrized systemsii. two oscillators: torus- en circle dynamicsiii. driven oscillators, examples:- Hopf-Neĭmark-Sacker bifurcation- parametric resonance- Hopf saddle-node bifurcation for mapsiv. universal properties for parameter space- resonance ∼ open & dense or residual- quasi-periodicity ∼ nowhere dense or meagrea fractal set of positive measure- and chaos emerging

What is resonance?Resonance: interaction of oscillating subsystems,whererational ratio of frequencies and withcompatible motionvoorbeelden:1 : 1 resonance: Huygens’s clocks,Moon and Earth, Charon and Pluto1 : 2 resonance: Botafumeiro(Santiago de Compostela)2 : 3 resonance: Mercury

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