This book contains an elaborated version of the lecture notes given at the Advanced Course on Geometry and Dynamics of Integrable Systems, held at the CRM in Barcelona.
Native to actual problem-solving problems in mechanics, the topic of Integrable Systems is currently on the crossroad of different disciplines in pure and applied mathematics, and it has important interactions with physics. The study of integrable systems has had special impact and also actively uses methods of Differential Geom...
This book contains an elaborated version of the lecture notes given at the Advanced Course on Geometry and Dynamics of Integrable Systems, held at the CRM in Barcelona.
Native to actual problem-solving problems in mechanics, the topic of Integrable Systems is currently on the crossroad of different disciplines in pure and applied mathematics, and it has important interactions with physics. The study of integrable systems has had special impact and also actively uses methods of Differential Geometry. 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). Therefore, these notes will attract experts from different backgrounds.
These notes concentrate on three different aspects of integrable systems: obstructions to integrability coming from Differential Galois theory, description of singularities of integrable systems using their relation to bi-Hamiltonian systems, and generalization of integrable systems to the non-Hamiltonian settings. The three parts are written by top experts in these fields.
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