Geometry and Dynamics of Integrable Systems

This book contains an elaborated version of the lecture notes given at the Advanced Course on Geometry andDynamics of Integrable Systems, held at the CRM in Barcelona.

Native to actualproblem-solving problems in mechanics, the topic of Integrable Systems iscurrently on the crossroad of different disciplines in pure and appliedmathematics, and it has important interactions with physics. The study of integrable systems has had special impactand also activelyuses methods of Differential Geometry. It isextremely important in SymplecticGeometry and Hamiltonian Dynamics, and has strong correlations with MathematicalPhysics, 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 integrablesystems: obstructions to integrabilitycoming from Differential Galois theory, descriptionof singularities of integrable systems using their relation to bi-Hamiltonian systems, and generalization ofintegrable systems to the non-Hamiltonian settings. The three parts are writtenby top experts in these fields.

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

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

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