By Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung,Eva Miranda,Vladimir Matveev
Based on lectures given at a complicated path on integrable structures on the Centre de Recerca Matemàtica in Barcelona, those lecture notes tackle 3 significant facets of integrable platforms: obstructions to integrability from differential Galois conception; the outline of singularities of integrable structures at the foundation in their relation to bi-Hamiltonian structures; and the generalization of integrable structures to the non-Hamiltonian settings. All 3 sections have been written through most sensible specialists of their respective fields.
Native to real problem-solving demanding situations in mechanics, the subject of integrable platforms is at the moment on the crossroads of a number of disciplines in natural and utilized arithmetic, and in addition has vital interactions with physics. The research of integrable platforms additionally actively employs tools from differential geometry. additionally, this can be very very important in symplectic geometry and Hamiltonian dynamics, and has robust correlations with mathematical physics, Lie idea and algebraic geometry (including replicate symmetry). As such, the booklet will entice specialists with a variety of backgrounds.
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