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Geometry and Dynamics of Integrable Systems

  • Alexey Bolsinov
  • Juan J. Morales-Ruiz
  • Nguyen Tien Zung
  • Eva Miranda
  • Vladimir Matveev

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Juan J. Morales-Ruiz
    Pages 1-33
  3. Nguyen Tien Zung
    Pages 85-140

About this book

Introduction

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.

Keywords

bi-Hamiltonian systems Poisson pencils non-Hamiltonian systems singularities Picard-Vessiot Differential Galois theory

Authors and affiliations

  • Alexey Bolsinov
    • 1
  • Juan J. Morales-Ruiz
    • 2
  • Nguyen Tien Zung
    • 3
  1. 1.School of MathematicsLoughborough UniversityLeicestershireUnited Kingdom
  2. 2.Escuela Superior de Ingenieros de Caminos, Canales y PuertosUniversidad Politécnica de MadridMadridSpain
  3. 3.Institut de MathématiquesUniversité Paul SabatierToulouseFrance

Editors and affiliations

  • Eva Miranda
    • 1
  • Vladimir Matveev
    • 2
  1. 1.Departamento de Matemàtica AplicadaUniversitat Politècnica de Catalunya Departamento de Matemàtica AplicadaBarcelonaSpain
  2. 2.Institut für MathematikFriedrich-Schiller-Universität Jena Institut für MathematikJenaGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-33503-2
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-33502-5
  • Online ISBN 978-3-319-33503-2
  • Series Print ISSN 2297-0304
  • Series Online ISSN 2297-0312
  • Buy this book on publisher's site