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Evolution of measures in the phase space of nonlinear Hamiltonian systems. (English) Zbl 1178.37049
Theor. Math. Phys. 136, No. 3, 1325-1335 (2003); translation from Teor. Mat. Fiz. 136, No. 3, 496-506 (2003).
Summary: We establish the existence of weak limits of solutions (in the class \(L _{p}, p\geq 1\)) of the Liouville equation for nondegenerate quasihomogeneous Hamilton equations. We find the limit probability distributions in the configuration space. We give conditions for a uniform distribution of Gibbs ensembles for geodesic flows on compact manifolds.

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
37A30 Ergodic theorems, spectral theory, Markov operators
70H05 Hamilton’s equations
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