Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
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DOI：
10.1007/978-1-4757-4073-8
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发表时间：
1991-12
期刊：
影响因子：
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通讯作者：
K. Meyer;G. R. Hall
中科院分区：
文献类型：
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作者：
K. Meyer;G. R. Hall
哈密顿系统的理论是一个庞大的课题，可以从许多不同的角度进行研究。这本书发展的基本理论的哈密顿微分方程从动力系统的观点。在第三版中，前四章为汉密尔顿理论和天体力学奠定了坚实的基础，使其适合高年级本科生或刚开始的研究生课程。它包含了一个扩展的处理限制性三体问题，包括一个新的推导，希尔的地区，离散对称性，以及更多的治疗。它还详细介绍了对称性，矩映射，Noether定理和Meyer-Marsden-Weinstein约化定理及其在三体问题中的应用。还包括一个介绍奇异减少和orbifolds与应用程序的周期解的分支沿沿着与介绍双纽线函数用于有界和稳定的结果。
The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. In this third edition, the first four chapters give a sound grounding in Hamiltonian theory and celestial mechanics making it suitable for an advanced undergraduate or beginning graduate course. It contains an expanded treatment of the restricted three-body problem including a new derivation, a treatment of Hill’s regions, discrete symmetries, and more. It also has a detailed presentation of the symmetries, the moment map, Noether’s theorem, and the Meyer-Marsden-Weinstein reduction theorem with applications to the three-body problem. Also included is an introduction to singular reduction and orbifolds with application to bifurcation of periodic solutions along with an introduction of the lemniscate functions used for bounded and stability results.