Abstract
We establish the existence of weak limits of solutions (in the class L p, p%thinsp;≥ 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.
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Kozlov, V.V., Treshchev, D.V. Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems. Theoretical and Mathematical Physics 136, 1325–1335 (2003). https://doi.org/10.1023/A:1025607517444
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DOI: https://doi.org/10.1023/A:1025607517444