This book explores the foundations of hamiltonian dynamical systems andstatistical mechanics in particular phase transitions from the point of viewof geometry a... » 

This book explores the foundations of hamiltonian dynamical systems andstatistical mechanics in particular phase transitions from the point of viewof geometry and topology. A broad participation of topology in these fields hasbeen lacking and this book will provide a welcome overview of the currentresearch in the area in which the author himself is a pioneer. Usinggeometrical thinking to solve fundamental problems in these areas compared tothe purely analytical methods usually used in physics could be highlyproductive. The author skillfully guides the reader whether mathematician orphysicists through the background needed to understand and use thesetechniques. TOCForeword. Preface. Introduction. Background in Physics.Geometrization of Hamiltonian Dynamics. Integrability. Geometry and chaos.Geometry of chaos and phase transitions. Topological Hypothesis on the originof phase transitions. Geometry topology and thermodynamics. Phasetransitions and topology necessity theorems. Phase transitions and topologyexact results. Future developments. Appendix 1 Elements of geometry andtopology of differentiable manifolds. Appendix 2 Elements of Riemanniangeometry. Appendix 3 Summary of elementary Morse theory. References. «