Geodesic
The functional mechanics: Evolution of the moments of distribution function and the Poincar\'e recurrence theorem
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 124-133

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One of modern approaches to a problem of the coordination of classical mechanics and the statistical physics — the functional mechanics is considered. Deviations from classical trajectories are calculated and evolution of the moments of distribution function is constructed. The relation between the received results and absence of paradox of Poincaré–Zermelo in the functional mechanics is discussed. Destruction of periodicity of movement in the functional mechanics is shown and decrement of attenuation for classical invariants of movement on a trajectory of functional mechanical averages is calculated.
Keywords: classical mechanics, irreversibility problem
Mots-clés : Liouville equation. 
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     author = {A. I. Mikhailov},
     title = {The functional mechanics: {Evolution} of the moments of distribution function  and the {Poincar\'e} recurrence theorem},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {124--133},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a16/}
}
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A. I. Mikhailov. The functional mechanics: Evolution of the moments of distribution function  and the Poincar\'e recurrence theorem. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 124-133. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a16/