Geometry and Dynamics of Integrable Systems

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Synopsis

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.

Book details

Edition:
1st ed. 2016
Series:
Advanced Courses in Mathematics - CRM Barcelona
Author:
Alexey Bolsinov, Juan J. Morales-Ruiz, Nguyen Tien Zung
ISBN:
9783319335032
Related ISBNs:
9783319335025
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
No
Date of addition:
2019-09-19
Usage restrictions:
Copyright
Copyright date:
2016
Copyright by:
N/A 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction