可積分系の幾何学：入門テキスト Geometry of Integrable Systems : An Introduction (Latin American Mathematics Series)

Arsie, Alessandro/ Mencattini, Igor

Springer International Publishing AG（2026/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 564 p.
• 商品コード 9783031962813

Full 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.