Geodesic
Dissipation effects in infinite-dimensional Hamiltonian systems.
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 1, pp. 78-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that the potential coupling of classical mechanical systems (an oscillator and a heat bath), one of which (the heat bath) is linear and infinite-dimensional, can provoke energy dissipation in a finite-dimensional subsystem (the oscillator). Under natural assumptions, the final dynamics of an oscillator thus reduces to a tendency toward equilibrium. D. V. Treschev previously obtained results concerning the dynamics of an oscillator with one degree of freedom and a quadratic or (under some additional assumptions) polynomial potential. Later, A. V. Dymov considered the case of a linear oscillator with an arbitrary (finite) number of degrees of freedom. We generalize these results to the case of a heat bath (consisting of several components) and a multidimensional oscillator (either linear or nonlinear).
Keywords: Lagrange system, system with infinite number of degrees of freedom, final dynamics. 
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S. M. Saulin. Dissipation effects in infinite-dimensional Hamiltonian systems.. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 1, pp. 78-99. http://geodesic.mathdoc.fr/item/TMF_2017_191_1_a5/

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