EAN: 9783319335025

ADVANCED COURSES IN MATHEMATICS - CRM BARCELONA...

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.

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