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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

  • Book
  • © 1992

Overview

Authors:
  1. Kenneth R. Meyer

    1. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Glen R. Hall

    1. Mathematics Department, Boston University, Boston, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Applied Mathematical Sciences (AMS, volume 90)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Hamiltonian Differential Equations and the N-Body Problem

    • Kenneth R. Meyer, Glen R. Hall
    Pages 1-32

  3. Linear Hamiltonian Systems

    • Kenneth R. Meyer, Glen R. Hall
    Pages 33-71

  4. Exterior Algebra and Differential Forms

    • Kenneth R. Meyer, Glen R. Hall
    Pages 72-86

  5. Symplectic Transformations and Coordinates

    • Kenneth R. Meyer, Glen R. Hall
    Pages 87-108

  6. Introduction to the Geometric Theory of Hamiltonian Dynamical Systems

    • Kenneth R. Meyer, Glen R. Hall
    Pages 109-153

  7. Continuation of Periodic Solutions

    • Kenneth R. Meyer, Glen R. Hall
    Pages 154-167

  8. Perturbation Theory and Normal Forms

    • Kenneth R. Meyer, Glen R. Hall
    Pages 168-200

  9. Bifurcations of Periodic Orbits

    • Kenneth R. Meyer, Glen R. Hall
    Pages 201-226

  10. Stability and KAM Theory

    • Kenneth R. Meyer, Glen R. Hall
    Pages 227-240

  11. Twist Maps and Invariant Curves

    • Kenneth R. Meyer, Glen R. Hall
    Pages 241-278

  12. Back Matter

    Pages 279-294
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Keywords

About this book

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. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.

Reviews

From the reviews of the second edition:

"The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. … It is a well-organized and accessible introduction to the subject … . This is an attractive book … ." (William J. Satzer, The Mathematical Association of America, March, 2009)

Authors and Affiliations

  • Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

    Kenneth R. Meyer

  • Mathematics Department, Boston University, Boston, USA

    Glen R. Hall

Bibliographic Information

  • Book Title: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

  • Authors: Kenneth R. Meyer, Glen R. Hall

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4757-4073-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1992

  • eBook ISBN: 978-1-4757-4073-8Published: 17 April 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XII, 294

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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