Advanced Courses in Mathematics - CRM Barcelona

Geometry and Dynamics of Integrable Systems

Authors: Bolsinov, Alexey, Morales-Ruiz, Juan J., Zung, Nguyen Tien

Editors: Miranda, Eva, Matveev, Vladimir (Eds.)

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  • Provides a clear introduction to Differential Galois Theory and to Picard-Vessiot Theory
  • Establishes, as a first book, a connection between Singularities of bi-Hamiltonian systems, stability analysis, and Poisson pencils
  • Shows how to apply the tools used in integrable Hamiltonian systems to integrable non-Hamiltonian systems, with applications in Control Theory, economics, and biology
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eBook 20,22 €
price for Spain (gross)
  • ISBN 978-3-319-33503-2
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Softcover 25,99 €
price for Spain (gross)
  • ISBN 978-3-319-33502-5
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About this Textbook

Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields.

Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.

About the authors

Juan J. Morales-Ruiz is Professor of Mathematics at Universidad Politécnica de Madrid.

Alexey Bolsinov is Reader in Mathematics at Loughborough University in Leicestershire.

Nguyen Tien Zung is Professor of Mathematics at University of Toulouse.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook 20,22 €
price for Spain (gross)
  • ISBN 978-3-319-33503-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 25,99 €
price for Spain (gross)
  • ISBN 978-3-319-33502-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Geometry and Dynamics of Integrable Systems
Authors
Editors
  • Eva Miranda
  • Vladimir Matveev
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-33503-2
DOI
10.1007/978-3-319-33503-2
Softcover ISBN
978-3-319-33502-5
Series ISSN
2297-0304
Edition Number
1
Number of Pages
VIII, 140
Number of Illustrations
19 b/w illustrations, 3 illustrations in colour
Topics