Latin American Mathematics Series: An Introduction

Arsie, Alessandro; Mencattini, Igor

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.

Details

Published by: Springer

Publication Date: 2026-01-10

Format: Hardcover

ISBN-13: 9783031962813

DOI: 10.1007/978-3-031-96282-0

Dimensions: 235cm x155cm

Pages: 564