{"product_id":"geometry-of-integrable-systems-an-introduction-9783031962813","title":"Geometry of Integrable Systems: An Introduction","description":"\u003cp\u003e • Author(s): Alessandro Arsie | Igor Mencattini\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Geometry - Differential\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003ePart 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.\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":47572203864215,"sku":"9783031962813","price":5204.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783031962813.webp?v=1774889243","url":"https:\/\/atlanticbooks.com\/products\/geometry-of-integrable-systems-an-introduction-9783031962813","provider":"Atlantic Books","version":"1.0","type":"link"}