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.
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