TY - BOOK ID - 7687512 TI - Geometry and Dynamics of Integrable Systems AU - Bolsinov, Alexey. AU - Morales-Ruiz, Juan J. AU - Zung, Nguyen Tien. AU - Miranda, Eva. AU - Matveev, Vladimir. PY - 2016 SN - 3319335022 3319335030 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Mathematics. KW - Algebra. KW - Field theory (Physics). KW - Dynamics. KW - Ergodic theory. KW - Differential geometry. KW - Dynamical Systems and Ergodic Theory. KW - Differential Geometry. KW - Field Theory and Polynomials. KW - Differential geometry KW - Ergodic transformations KW - Dynamical systems KW - Kinetics KW - Classical field theory KW - Continuum physics KW - Math KW - Differentiable dynamical systems. KW - Global differential geometry. KW - Physics KW - Continuum mechanics KW - Geometry, Differential KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Geometry, Algebraic. KW - Mathematics KW - Mathematical analysis KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:7687512 AB - Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemà tica 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. ER -