Hamiltonian Structures and Generating Families

  • Sergio Benenti

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sergio Benenti
    Pages 1-25
  3. Sergio Benenti
    Pages 27-30
  4. Sergio Benenti
    Pages 57-76
  5. Sergio Benenti
    Pages 77-88
  6. Sergio Benenti
    Pages 121-152
  7. Sergio Benenti
    Pages 153-205
  8. Sergio Benenti
    Pages 207-225
  9. Back Matter
    Pages 247-258

About this book

Introduction

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)

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.

Keywords

Control of static mechanical systems Control of thermostatic systems Geometrical optics Hamilton-Jacobi equation Symplectic Relations Symplectic geometry

Authors and affiliations

  • Sergio Benenti
    • 1
  1. 1., Dipartimento di MatematicaUniversità di TorinoTorinoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1499-5
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1498-8
  • Online ISBN 978-1-4614-1499-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book