Central configurations, periodic orbits, and Hamiltonian systems [electronic resource]

• 作者： Llibre, Jaume.
• 其他作者：
  • Moeckel, Richard.
  • Simo, Carles.
  • SpringerLink (Online service)
• 其他題名：
  • Advanced courses in mathematics, CRM Barcelona
• 出版： Basel : Springer Basel :Imprint: Birkhauser
• 叢書名： Advanced courses in mathematics - CRM Barcelona
• 主題： Differentiable dynamical systems , Mathematics , Ordinary Differential Equations. , Dynamical Systems and Ergodic Theory. , Mathematical Applications in the Physical Sciences. , Mathematical Methods in Physics.
• ISBN： 9783034809337 (electronic bk.) 、 9783034809320 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 1 The Averaging Theory for Computing Periodic Orbits -- Introduction: the classical theory -- Averaging theory for arbitrary order and dimension -- Three applications of Theorem -- 2 Lectures on Central Configurations -- The n-body problem -- Symmetries and integrals -- Central configurations and self-similar solutions -- Matrix equations of motion -- Homographic motions of central configurations in Rd -- Albouy-Chenciner reduction and relative equilibria in Rd -- Homographic motions in Rd -- Central configurations as critical points -- Collinear central configurations -- Morse indices of non-collinear central configurations -- Morse theory for CC's and SBC's -- Dziobek configurations -- Convex Dziobek central configurations -- Generic finiteness for Dziobek central configurations -- Some open problems -- 3 Dynamical Properties of Hamiltonian Systems -- Introduction -- Low dimension -- Some theoretical results, their implementation and practical tools -- Applications to Celestial Mechanics.
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• 摘要註: The notes of this book originate from three series of lectures given at the Centre de Recerca Matematica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous differential systems in Rn via the Averaging Theory and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying Central Configurations. The last one, by Carles Simo, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems. The book is directed towards graduate students and researchers interested in dynamical systems, in particular in the conservative case, and aims at facilitating the understanding of dynamics of specific models. The results presented and the tools introduced in this book include a large range of applications.
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