Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
Résumé
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 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 physicist, through the background
needed to understand and use these techniques.