Titlebook: Dynamical System and Chaos; An Introduction with Rui Dil?o Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive l

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Alexandra Lindner,Michael StadtelmannWe review elementary results on the geometric theory of Hamiltonian dynamical systems. We discuss the Denjoy theory of circle maps as a preparation for the KAM interpretation of instabilities and resonances of Hamiltonian systems.

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EXTOL

Brigitte Falkenburg,Margaret MorrisonIn this introductory text to celestial mechanics, we review the general problem of . bodies, the Kepler problem, the three-body problem, the restricted three-body problem, the Sitnikov problem and the Keplerian dumbbell, a simple model for the spin-orbit interaction. The existence of chaotic trajectories in the solar system is discussed.

男學(xué)院

Maschinelles Lernen – Roboter in der SchuleWe introduce basic techniques of nonlinear control theory from the perspective of the Pontriaguine maximum principle. We analyse in detail systems from physics, celestial mechanics and macroeconomics.

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Hamiltonian SystemsWe review elementary results on the geometric theory of Hamiltonian dynamical systems. We discuss the Denjoy theory of circle maps as a preparation for the KAM interpretation of instabilities and resonances of Hamiltonian systems.

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Synchronisation of?Clocks and?PendulumsWe analyse Huygens’s two-clock system and give conditions for anti-phase and in-phase synchronisation. We prove the robustness of anti-phase synchronisation. We analyse the conditions of anti-phase synchronisation of pendulum systems.

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Introduction to Celestial MechanicsIn this introductory text to celestial mechanics, we review the general problem of . bodies, the Kepler problem, the three-body problem, the restricted three-body problem, the Sitnikov problem and the Keplerian dumbbell, a simple model for the spin-orbit interaction. The existence of chaotic trajectories in the solar system is discussed.

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https://doi.org/10.1007/978-3-031-25154-2Dynamical chaos theory; Applications of dynamical systems; Celestial mechanics; Centre Manifold; Poincar

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978-3-031-25156-6The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl