Overview

"This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to be stated, proved, and understood in a much easier and elegant way. From the reviews of the Russian edition: ""The main accent is shifted to the application . . . in geometrical optics, thermostatics and control theory, and not to the Hamiltonian mechanics only. . . . To make the book fairly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course in geometry. The excellent collection of examples illustrates the relatively hard and highly abstract mathematical theory and its hidden difficulties. . . . The book can rise real interest for specialists . . . .  The . . . book is a significant input in the modern symplectic geometry and its applications."" (Andrey Tsiganov, St. Petersburg State University)"

Full Product Details

Author:   Sergio Benenti
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2011
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9781461414988

ISBN 10:   1461414989
Pages:   258
Publication Date:   08 September 2011
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Language:   English

Table of Contents

Preface.- Basic Notions of Calculus on Manifolds.- Relations.- Symplectic Relations on Symplectic Manifolds.- Symplectic Relations on Cotangent Bundles.- Canonical Lift on Cotangent Bundles.-The Geometry of the Hamilton-Jacobi Equation.- Hamiltonian Optics in Euclidean Spaces.- Control of Static Systems.- Supplementary Topics.- Global Hamilton Principal Functions on S2 and H2.- References.- Index.

Reviews

From the reviews of the Russian edition: !In this book the main accent is shifted to the application of modern mathematical methods of symplectic geometry and topology in geometrical optics, thermostatics and control theory, and not to the Hamiltonian mechanics only. ! To make the book fairly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course in geometry. The excellent collection of examples illustrates the relatively hard and highly abstract mathematical theory and its hidden difficulties. !The book can rise real interest for specialists, as the presentation follows the best classical traditions of Italian geometric school (Levi-Civita, etc) and differs from the style of Russian mathematics. The ! book is a significant input in the modern symplectic geometry and its applications! (Andrey Tsiganov, St. Petersburg State University)

From the reviews of the Russian edition: !In this book the main accent is shifted to the application of modern mathematical methods of symplectic geometry and topology in geometrical optics, thermostatics and control theory, and not to the Hamiltonian mechanics only. ! To make the book fairly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course in geometry. The excellent collection of examples illustrates the relatively hard and highly abstract mathematical theory and its hidden difficulties. !The book can rise real interest for specialists, as the presentation follows the best classical traditions of Italian geometric school (Levi-Civita, etc) and differs from the style of Russian mathematics. The ! book is a significant input in the modern symplectic geometry and its applications! (Andrey Tsiganov, St. Petersburg State University)

Author Information

Sergio Benenti is a professor of mathematical physics at Università di Torino, Italy. His current fields of research include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differential equations of physics, and mathematical models of the dynamics of non-holonomic systems.

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