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Lecture Notes in Mathematics Lecture Notes in Mathematics - English

Metamorphoses of Hamiltonian Systems with Symmetries

Authors: Efstathiou, Konstantinos

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  • ISBN 978-3-540-31550-6
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Softcover $49.95
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About this book

Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Reviews

From the reviews of the first edition:

"This is a well-written book which utilizes modern methods of classical mechanics in the study of four physical Hamiltonian systems with symmetries … . Two appendices are included for completeness. … This book is likely to appeal to specialists in the area." (F. M. Mahomed, Zentralblatt MATH, Vol. 1069, 2005)


Table of contents (8 chapters)

  • Introduction

    Efstathiou, Konstantinos

    Pages 1-8

  • 1. Four Hamiltonian Systems

    Efstathiou, Konstantinos

    Pages 9-33

  • 2. Small Vibrations of Tetrahedral Molecules

    Efstathiou, Konstantinos

    Pages 35-58

  • 3. The Hydrogen Atom in Crossed Fields

    Efstathiou, Konstantinos

    Pages 59-85

  • 4. Quadratic Spherical Pendula

    Efstathiou, Konstantinos

    Pages 87-111

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-540-31550-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-24316-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Metamorphoses of Hamiltonian Systems with Symmetries
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1864
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-31550-6
DOI
10.1007/b105138
Softcover ISBN
978-3-540-24316-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 149
Topics