TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
T2  - Interdisciplinary Applied Mathematics,
SN  - 9780387499574
AV  - QA313 
U1  - 515.39 23
PY  - 2007///
CY  - New York, NY
PB  - Springer New York
KW  - Mathematics
KW  - Differentiable dynamical systems
KW  - Quantum theory
KW  - Mathematical physics
KW  - Dynamical Systems and Ergodic Theory
KW  - Mathematical Methods in Physics
KW  - Quantum Physics
KW  - Applications of Mathematics
KW  - Statistical Physics, Dynamical Systems and Complexity
N1  - Background in Physics -- Geometrization of Hamiltonian Dynamics -- Integrability -- Geometry and Chaos -- Geometry of Chaos and Phase Transitions -- Topological Hypothesis on the Origin -- Geometry, Topology and Thermodynamics -- Phase Transitions and Topology: Necessity Theorems -- Phase Transitions and Topology: Exact Results -- Future Developments; ZDB-2-SMA
N2  - 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 " 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
UR  - http://dx.doi.org/10.1007/978-0-387-49957-4
ER  -