Chaos

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This twelfth volume in the Poincaré Seminar Series offers an interdisciplinary perspective on the concept of Chaos in both classical and quantum mechanics. It addresses significant scientific questions, from identifying classical chaotic dynamics in quantum systems to predicting the fate of our planetary system. The seven articles are pedagogical, originating from lectures aimed at a broad scientific audience. Notable contributions include É. Ghys's comprehensive description of the Lorenz attractor and the Lorenz butterfly effect, highlighting key mathematical issues in deterministic chaos. S. Fauve details the von Kármán Sodium experiment, which demonstrated the spontaneous generation of a magnetic field in turbulent flow, mirroring Earth's magnetic field. U. Smilansky presents a toy model that elucidates quantum chaos and its connection to random matrix theory. P. Bourgade and J. P. Keating explore the link between the Riemann ζ-function's zeros and the statistics of eigenvalues of random unitary matrices, potentially leading to a proof of the Riemann Hypothesis. H-J. Stöckmann discusses experimental validations of theoretical predictions in quantum chaos, while S. Nonnenmacher examines the eigenmodes of quantized chaotic systems. Lastly, J. Laskar reviews the stability and fate of our chaotic Solar system, including estimates of potential planetary collisions. This volume is of broad interest to physicists and mathematician