Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

• Main Author: Pettini, Marco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2007.
• Series: Interdisciplinary Applied Mathematics, 33
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Applied mathematics.; Engineering mathematics.; Physics.; Quantum physics.; Statistical physics.; Dynamical systems.; Dynamical Systems and Ergodic Theory.; Mathematical Methods in Physics.; Quantum Physics.; Applications of Mathematics.; Statistical Physics, Dynamical Systems and Complexity.

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 curr...

Table of Contents:

• 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.