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This book includes lectures given at the DMV seminar “Classical Nonintegrability, Quantum Chaos”, and the aim of it is to provide an introduction to the ideas and mathematical techniques of classical and quantum nonlinear dynamics. The section by Viviane Baladi gives an overview of the current literature and includes a discussion of the problems and results in that literature. The chapters on irregular scattering and expanding maps illustrate techniques in nonlinear dynamics using simple but nontrivial examples. The chapters on quantum chaos and on Liouville surfaces emphasize a phase space geometry approach to semi-classical quantum theory.
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