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Mathematics and its Applications

Integrability and Nonintegrability in Geometry and Mechanics

Authors: Fomenko, A.T.

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About this book

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Reviews

'...we consider this book to be a valuable contribution to present mathematics. It is useful primarily for researchers in the field but it may just as ell be used by students of mathematics, mechanics, or physics and by anybody interested in the modern applications of geometry and topology.' Acta Applicandae Mathematicae 28 1992

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Some Equations of Classical Mechanics and Their Hamiltonian Properties

    Pages 1-54

    Fomenko, A. T.

  • The Theory of Surgery on Completely Integrable Hamiltonian Systems of Differential Equations

    Pages 55-142

    Fomenko, A. T.

  • Some General Principles of Integration of Hamiltonian Systems of Differential Equations

    Pages 143-186

    Fomenko, A. T.

  • Integration of Concrete Hamiltonian Systems in Geometry and Mechanics. Methods and Applications

    Pages 187-255

    Fomenko, A. T.

  • Nonintegrability of Certain Classical Hamiltonian Systems

    Pages 256-299

    Fomenko, A. T.

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-94-009-3069-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-90-277-2818-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-94-010-7880-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Integrability and Nonintegrability in Geometry and Mechanics
Authors
Series Title
Mathematics and its Applications
Series Volume
31
Copyright
1988
Publisher
Springer Netherlands
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-94-009-3069-8
DOI
10.1007/978-94-009-3069-8
Hardcover ISBN
978-90-277-2818-0
Softcover ISBN
978-94-010-7880-1
Series ISSN
0169-6378
Edition Number
1
Number of Pages
XV, 343
Additional Information
Originally published in Russian
Topics

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