{ "item_title" : "Geometry of Integrable Systems", "item_author" : [" Alessandro Arsie", "Igor Mencattini "], "item_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. This 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. Part 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. This 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. ", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/3/03/196/281/3031962818_b.jpg", "price_data" : { "retail_price" : "69.99", "online_price" : "69.99", "our_price" : "69.99", "club_price" : "69.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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