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＜E-Book＞
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics / by Marco Pettini
(Interdisciplinary Applied Mathematics. ISSN:21969973 ; 33)

Edition	1st ed. 2007.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2007
Language	English
Size	XVI, 456 p. 91 illus : online resource
Authors	*Pettini, Marco author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Mathematical physics LCSH:Quantum physics LCSH:Mathematics LCSH:System theory FREE:Dynamical Systems FREE:Mathematical Methods in Physics FREE:Quantum Physics FREE:Applications of Mathematics FREE:Complex Systems FREE:Theoretical, Mathematical and Computational Physics
Notes	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 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 â€" 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 HTTP:URL=https://doi.org/10.1007/978-0-387-49957-4

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