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＜電子ブック＞
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem / by Kenneth Meyer, Glen Hall, Dan Offin
(Applied Mathematical Sciences. ISSN:2196968X ; 90)

版	2nd ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIII, 399 p : online resource
著者標目	*Meyer, Kenneth author Hall, Glen author Offin, Dan author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Mathematical physics LCSH:Mathematical analysis FREE:Dynamical Systems FREE:Theoretical, Mathematical and Computational Physics FREE:Analysis
一般注記	Hamiltonian Systems -- Equations of Celestial Mechanics -- Linear Hamiltonian Systems -- Topics in Linear Theory -- Exterior Algebra and Differential Forms -- Symplectic Transformations -- Special Coordinates -- Geometric Theory -- Continuation of Solutions -- Normal Forms -- Bifurcations of Periodic Orbits -- Variational Techniques -- Stability and KAM Theory -- Twist Maps and Invariant Circle This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, the basics of the symplectic group, an introduction to reduction, applications of Poincaré's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapter devoted to finding symmetric periodic solutions by calculus of variations methods. The main examples treated in this text are the N-body problem and various specialized problems like the restricted three-body problem. The theory of the N-body problem is used to illustrate the general theory. Some of the topics covered are the classical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods, stability and instability of the Lagrange triangular point. Ken Meyer is an emeritus professor at the University of Cincinnati, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen's University HTTP:URL=https://doi.org/10.1007/978-0-387-09724-4

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