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© 2007

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

  • The subject of the book is very original and nothing similar has been written hitherto

  • Will be of interest to both mathematicians and physicists

  • Numerous illustrations throughout

Book

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 33)

Table of contents

About this book

Introduction

This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transition, from the point of view of geometry and topology. A broad participation of topology in these fields has been lacking and this book will provide a welcome overview of the current research in the area, in which the author himself is a pioneer. Using geometrical thinking to solve fundamental problems in these areas, compared to the purely analytical methods usually used in physics could be highly productive. The author skillfully guides the reader, whether mathematician or physicists through the background needed to understand and use these techniques.

Dr. Marco Pettini is affiliated with the Istituto Nazionale di Astrofisica â€" Osservatorio Astrofisico di Arretri in Firenze, Italy.

From the foreword:

"It is in particular the quality of mind of the author and his deep physical, as well as mathematical insights, which make this book so special and inspiring. It is a "must" for those who want to venture into a new approach to old problems or want to use new tools for new problems." -- Professor E. G. D. Cohen, Rockefellar University, New York.

Keywords

Dynamics Geometry Hamiltonian Pettini dynamical systems topology

Authors and affiliations

  1. 1.Osservatorio Astrofisico di ArcetriFirenzeItaly

About the authors

The author is one of few pioneering individuals in this recently emerged important research area. His book will be a unique contribution to the field.

Bibliographic information

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Reviews

From the reviews:

"The present book is an excellent synthesis of two basic topics in classical applied mathematics: Hamiltonian dynamics, with a special view towards the Hamiltonian chaos, and statistical mechanics, mainly for what concerns phase transition phenomena in systems described by realistic intermolecular or interatomic forces. The perfect conclusion appears in a Foreword written by E.G.D. Cohen: "this book makes a courageous attempt to clarify these fundamental phenomena in a new way.""

-Zentralblatt Math