Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
-16 %

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

 Previously published in hardcover
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ISBN-13:
9781441921642
Einband:
Previously published in hardcover
Erscheinungsdatum:
23.11.2010
Seiten:
472
Autor:
Marco Pettini
Gewicht:
707 g
Format:
235x155x25 mm
Sprache:
Englisch
Beschreibung:

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The subject of the book, which contains numerous illustrations throughout, is very original and nothing similar has been written hitherto.
This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The subject of the book, which contains numerous illustrations throughout, is very original and nothing similar has been written hitherto.
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.