Oscillator and thermostat

Dmitry Treschev

doi:10.3934/dcds.2010.28.1693

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2010, Volume 28, Issue 4: 1693-1712. Doi: 10.3934/dcds.2010.28.1693

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Oscillator and thermostat

Dmitry Treschev^1,

1.
Steklov Mathematical Institute, Gubkina str., Moscow, 119991

Received: September 30, 2009

Revised: January 31, 2010

Published: November 2010

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Abstract

We study the problem of a potential interaction of a finite- dimensional Lagrangian system (an oscillator) with a linear infinite-dimensional one (a thermostat). In spite of the energy preservation and the Lagrangian (Hamiltonian) nature of the total system, under some natural assumptions the final dynamics of the finite-dimensional component turns out to be simple while the thermostat produces an effective dissipation.

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Mathematics Subject Classification: Primary: 37K; Secondary: 70H.

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