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Home > Reference Books > Research and information: general > Information theory > Cybernetics and systems theory > Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics: (33 Interdisciplinary Applied Mathematics)
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics: (33 Interdisciplinary Applied Mathematics)

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics: (33 Interdisciplinary Applied Mathematics)


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About the Book

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The subject of the book is very original and nothing similar has been written hitherto. There are numerous illustrations throughout and the book will be of interest to both mathematicians and physicists. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The two areas are strongly related because the geometrization of microscopic dynamics, which is the ultimate physical source of phase transitions, naturally leads to investigate how geometry and topology of the mechanical manifolds have to change to induce a phase transition.



Table of Contents:
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.

About the Author :
The author is one of few pioneering individuals in this recently emerged important research area. His book will be a unique contribution to the field.

Review :
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


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Product Details
  • ISBN-13: 9781441921642
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 453
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 1441921648
  • Publisher Date: 23 Nov 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 33 Interdisciplinary Applied Mathematics


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Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics: (33 Interdisciplinary Applied Mathematics)
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Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics: (33 Interdisciplinary Applied Mathematics)
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