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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

Author: Kenneth MeyerLawrence SirovichJerrold E MarsdenS S AntmanJack HaleAll authors
Publisher: New York, NY : Springer New York, 2009.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), 90.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kenneth Meyer; Lawrence Sirovich; Jerrold E Marsden; S S Antman; Jack Hale; Glen Hall; Philip Holmes; James Keener; Angela Stevens; Reinhard Laubenbacher; Bernard Matkowsky; Alexander Mielke; Dan Offin; Charles Peskin; K R Sreenivasan; Julien Keller
ISBN: 9780387097244 0387097244
OCLC Number: 311304499
Description: 1 online resource (: v.: digital.
Contents: Hamiltonian Differential Equations and the N-Body Problem --
Exterior Algebra and Differential Forms --
Symplectic transformations and coordinates --
Introduction to the Geometric Theory of Hamiltonian Dynamical Systems --
Continuation of Periodic Solutions --
Perturbation Theory and Normal Forms --
Bifurcations of Periodic Orbits --
Stability and KAM Theory --
Twist Maps and Invariant Curves.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), 90.
Responsibility: by Kenneth Meyer, Glen Hall, Dan Offin ; edited by Jack Hale, Philip Holmes, James Keener, Julien Keller, Reinhard Laubenbacher, Bernard Matkowsky, Alexander Mielke, Charles Peskin, K.R. Sreenivasan, Angela Stevens, Stuart Antman, Jerrold E. Marsden, Lawrence Sirovich.

Abstract:

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.

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