Overview
- Enhanced version of Russian first edition
- Focuses on Hamiltonian mechanics, as well as the application of modern mathematical methods of symplectic geometry and topology in geometrical optics, thermostatics and control theory
- Self-contained with full details of basic notions of calculus on manifolds in the first two chapters
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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About this book
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)
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Keywords
Table of contents (10 chapters)
Reviews
From the reviews:
“This book gives the basic definitions and results as well as some physical instances where the theory is applied, of Hamiltonian systems in terms of Lagrangian submanifolds and their generating families. … This new work gives an improved presentation of the theoretical part and deeper developments of its applications. … This book is aimed at both undergraduate and graduate students … in Algebra and Geometry. … Specialists will also find a nice reference in this book … .” (Marco Castrillon Lopez, The European Mathematical Society, May, 2013)
“The book under review is an enhanced version of a first edition in Russian; it deals with Hamiltonian structures that are often encountered in mathematical models of different physical phenomena. … The reader can find substantial bibliography and a detailed index at the end. The book is well organized, the exposition is rigorous and clear. It should attract interest of graduate students and researchers interested in the modern symplectic geometry and its applications.” (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1233, 2012)
"…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 modernsymplectic geometry and its applications…” (Andrey Tsiganov, St. Petersburg State University)
Authors and Affiliations
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Bibliographic Information
Book Title: Hamiltonian Structures and Generating Families
Authors: Sergio Benenti
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-1499-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Softcover ISBN: 978-1-4614-1498-8Published: 08 September 2011
eBook ISBN: 978-1-4614-1499-5Published: 15 September 2011
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 258
Number of Illustrations: 50 b/w illustrations
Topics: Differential Geometry, Mathematical Applications in the Physical Sciences, Systems Theory, Control, Mathematical Physics, Global Analysis and Analysis on Manifolds