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December  2010, 28(4): 1693-1712. doi: 10.3934/dcds.2010.28.1693

Oscillator and thermostat

Dmitry Treschev 1,

1. 

Steklov Mathematical Institute, Gubkina str., Moscow, 119991

Received  October 2009 Revised  February 2010 Published  June 2010

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.
Keywords: Hamiltonian systems, final dynamics., Lagrangian systems.
Mathematics Subject Classification: Primary: 37K; Secondary: 70.
Citation: Dmitry Treschev. Oscillator and thermostat. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1693-1712. doi: 10.3934/dcds.2010.28.1693
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