Research Catalog

Title

Geometry and topology in Hamiltonian dynamics and statistical mechanics / Marco Pettini.

Author

Pettini, Marco.

Publication

New York : Springer, c2007.

Items in the Library & Off-site

Details

Description

xvi, 451 p. : ill.; 25 cm.

Summary

"This book explores the foundations of Hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, 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 an 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 guides the reader, whether mathematician or physicist, through the background needed to understand and use these techniques."--BOOK JACKET.

Series Statement

Interdisciplinary applied mathematics ; v. 33

Uniform Title

• Interdisciplinary applied mathematics v. 33.
• Interdisciplinary applied mathematics 33

Subjects

• Statistical Physics, Dynamical Systems and Complexity
• Applications of Mathematics
• Quantum Physics
• Mathematical Methods in Physics
• Dynamical Systems and Ergodic Theory
• Mathematical physics
• Quantum theory
• Differentiable dynamical systems
• Mathematics
• Statistical mechanics
• Hamiltonian systems

Bibliography (note)

• Includes bibliographical references (p. 431-439) and indexes.

Contents

Background in physics -- Geometrization of Hamiltonian dynamics -- Integrability -- Geometry and chaos -- Geometry of chaos and phase transitions -- Topological hypothesis on the origin of phase transitions -- Geometry, topology and thermodynamics -- Phase transitions and topology: necessity theorems -- Phase transitions and topology : exact results -- Future developments -- Appendix A : Elements of geometry and topology of differentiable manifolds -- Appendix B : Elements of Riemannian geometry -- Appendix C : Summary of elementary Morse theory.

ISBN

• 9780387308920 (hbk.)
• 038730892X (hbk.)
• 9780387499574 (e-book)
• 0387499571 (e-book)

LCCN

^^2007928914

OCLC

• 74966935
• SCSB-10309450

Owning Institutions

Harvard Library