Gibbs ensembles, equidistribution of the energy of sympathetic oscillators and statistical models of thermostat

Regular and Chaotic Dynamics

Volumn 13, Issue 3, 2008, Pages 141-154

  Kozlov, V V ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Hamiltonian system; Sympathetic oscillators; Thermostat; Weak convergence

Indexed keywords

EID: 45349090524     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1134/S1560354708030015     Document Type: Article

References (11)

1. Fermi, E., Pasta, J., and Ulam, S., Studies of Nonlinear Problems, Los Alamos Scientific Laboratory, Los Alamos, NM, 1955 (Reprinted in: Collected Works of Enrico Fermi, Vol. 2, University of Chicago Press, 1965).
2. Bogolubov, N.N., On Some Statistical Methods in Mathematical Physics, Kiev: Ukr. SSR Academy of Sciences, 1945.
3. Szász, D., Ed., Hard Ball Systems and the Lorentz Gas, vol. 101 of Encycl. of Math. Sciencies, Berlin: Springer-Verlag, 2000.
4. Kozlov, V.V., Thermal Equilibrium in the Sense of Gibbs and Poincaré, Dokl. Math., 2002, vol. 65, no. 1, pp. 125-128.
5. Kozlov, V.V. and Treschev, D.V., Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems, Teoret. Mat. Fiz., 2003, vol. 136, no. 3, pp. 496-506 [Engl. transl.: Theoret. and Math. Phys., 2003, vol. 136, no. 3, pp. 1325-1335].
6. Kozlov, V.V., Kinetics of Collisionless Continuous Medium, Regul. Chaotic Dyn., 2001, vol. 6, no. 3, pp. 235-251.
7. Kozlov, V.V. and Treschev, D.V., Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian systems, Teoret. Mat. Fiz., 2003, vol. 134, no. 3, pp. 388-400 [Engl. transl.: Theoret. and Math. Phys., 2003, vol. 134, no. 3, pp. 339-350].
8. Kozlov, V.V. and Treschev, D.V., On New Forms of the Ergodic Theorem, J. Dynam. Control Systems, 2003, vol. 9, no. 3, pp. 449-453.
9. Kozlov, V.V., Billiards, Invariant Measures, and Equilibrium Thermodynamics, II, Regul. Chaotic Dyn., 2004, vol. 9, no. 2, pp. 91-100.
10. Bogolubov, N.N., On Some Problems Connected with Validation of Statistical Mechanics, in: Bogolubov, N.N., Collected Works, Vol. VI, Moscow: Nauka, 2006, pp. 432-440.
11. Kozlov, V.V., Symmetries, Topology, and Resonances in Hamiltonian Mechanics, Berlin: Springer-Verlag, 1996.