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

Type

Book

Authors

Marco Pettini

ISBN 10

1402065353

ISBN 13

9781402065354

Tags

Differential Equations, Topology, Mathematical Analysis, Mathematical Physics, Quantum Theory, Geometry, Physics

Description

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. 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 book contains numerous illustrations throughout and it will interest both mathematicians and physicists. - from Amzon

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