Marco Pettini

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

• Broschiertes Buch

Produktbeschreibung

Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,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. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available.

Produktdetails

• Interdisciplinary Applied Mathematics 33
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-2164-2
• Softcover reprint of hardcover 1st ed. 2007
• Seitenzahl: 472
• Erscheinungstermin: 23. November 2010
• Englisch
• Abmessung: 235mm x 155mm x 26mm
• Gewicht: 709g
• ISBN-13: 9781441921642
• ISBN-10: 1441921648
• Artikelnr.: 32189937

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

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