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Equilibrium statistical solutions for dynamical systems with an infinite number of degrees of freedom. (English. Russian original) Zbl 0632.60108

Math. USSR, Sb. 58, 397-406 (1987); translation from Mat. Sb., Nov. Ser. 130(172), No. 3, 394-403 (1986).
The equilibrium (Gibbs) measures for classical dynamical systems with infinite degrees of freedom are defined without the existence assumption for the flow. It is shown that if the regular flow exists then the Gibbs measure satisfies the classical KMS condition. The relations of the presented formalism to Euclidean quantum field theory are indicated and a few examples of nonlinear wave equations are presented as an illustration.
Reviewer: R.Alicki

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B05 Classical equilibrium statistical mechanics (general)
47H20 Semigroups of nonlinear operators
35Q99 Partial differential equations of mathematical physics and other areas of application
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H99 Hamiltonian and Lagrangian mechanics
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