Titlebook: Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics; Marco Pettini Book 2007 Springer-Verlag New York 2007 Dynamics.Ge

Fretful

Integrability, methods and results. For example, as we have discussed in Chapter 2, the weaker requirement of only approximate integrability over finite times, or the existence of integrable regions in the phase space of a globally nonintegrable system, has led to the development of classical perturbation theory,

杀死

Geometry and Chaos, main tool, to reach a twofold objective: first, to obtain a deeper understanding of the origin of chaos in Hamiltonian systems, and second, to obtain quantitative information on the “strength” of chaos in these systems.

Brocas-Area

飞行员

Topological Hypothesis on the Origin,onspace curvature fluctuations) related to the Riemannian geometrization of the dynamics in configuration space.1 These quantities have been computed, using time averages, for many different models undergoing continuous phase transitions, namely . lattice models with discrete and continuous symmetri

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indigenous

Phase Transitions and Topology: Necessity Theorems,jecture the involvement of topology in phase transition phenomena— formulating what we called the .—and then provided both indirect and direct numerical evidence of this conjecture. The present chapter contains a major leap forward: the rigorous proof that topological changes of equipotential hypers

extinguish

Phase Transitions and Topology: Exact Results,o singularities in the . → .limit, which are used to define the occurrence of an equilibrium phase transition, is . due to appropriate topological transitions in configuration space. The relevance of topology is made especially clear by the explicit dependence of thermodynamic configurational entrop

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