Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

by Marco Pettini

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main 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.

456 pages, Hardcover

First published June 1, 2007