{"product_id":"alessandro-arsie-geometry-of-integrable-systems-9783031962813","title":"Geometry of Integrable Systems","description":"This textbook explores differential geometrical aspects of the theory of completely integrable Hamiltonian systems. It provides a comprehensive introduction to the mathematical foundations and illustrates it with a thorough analysis of classical examples.\n\u003cbr\u003e\nThis book is organized into two parts. Part I contains a detailed, elementary exposition of the topics needed to start a serious geometrical analysis of complete integrability. This includes a background in symplectic and Poisson geometry, the study of Hamiltonian systems with symmetry, a primer on the theory of completely integrable systems, and a presentation of bi-Hamiltonian geometry.\n\u003cbr\u003e\nPart II is devoted to the analysis of three classical examples of integrable systems. This includes the description of the (free) n-dimensional rigid-body, the rational Calogero-Moser system, and the open Toda system. In each case, ths system is described, its integrability is discussed, and at least one of its (known) bi-Hamiltonian descriptions is presented.\n\u003cbr\u003e\nThis work can benefit advanced undergraduate and beginning graduate students with a strong interest in geometrical methods of mathematical physics. Prerequisites include an introductory course in differential geometry and some familiarity with Hamiltonian and Lagrangian mechanics.","brand":"Springer","offers":[{"title":"Default Title","offer_id":53822409900374,"sku":null,"price":0.0,"currency_code":"EUR","in_stock":false}],"url":"https:\/\/www.momoxbooks.com\/products\/alessandro-arsie-geometry-of-integrable-systems-9783031962813","provider":"momoxbooks","version":"1.0","type":"link"}