Weak convergence of solutions of the Liouville equation for nonlinear Hamiltonian systems

Theoretical and Mathematical Physics

Volumn 134, Issue 3, 2003, Pages 339-350

  Kozlov, V V ^a   Treshchev, D V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Entropy; Hamiltonian system; Liouville equation; Weak convergence

Indexed keywords

EID: 0037226318     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022697321418     Document Type: Article

References (18)

1. J. W. Gibbs, "Elementary principles in statistical mechanics," in: The Collected Works of J. W. Gibbs, Vol. II, Part 1, Yale Univ. Press, New Haven, Conn. (1931).
2. N. N. Bogoliubov, Problems of a Dynamical Theory in Statistical Physics [in Russian], Gostekhizdat, Moscow (1946); English transl., North-Holland, Amsterdam (1962).
3. G. E. Uhlenbeck and G. W. Ford, Lectures in Statistical Mechanics (Lectures in Applied Mathematics. Proceedings of the Summer Seminar, Boulder, Colorado, 1960, Vol. 1), Amer. Math. Soc., Providence, R. I. (1963).
4. H. Poincaré, J. Phys. Théor. Appl., 4 Série, 5, 369-403 (1906).
5. P. R. Halmos, Lectures on Ergodic Theory, The Mathematical Society of Japan, Tokyo (1956); A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, Cambridge (1985).
6. P. R. Halmos, Lectures on Ergodic Theory, The Mathematical Society of Japan, Tokyo (1956); A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, Cambridge (1985).
7. V. V. Kozlov, Dokl. Rosaiiskoi Akad. Nauk, 382, 593 (2002).
8. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1949); English transl. (Princeton Math. Series), Princeton Univ. Press, Princeton, N. J. (1960).
9. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1949); English transl. (Princeton Math. Series), Princeton Univ. Press, Princeton, N. J. (1960).
10. G. H. Hardy, Divergent Series, Clarendon, Oxford (1949).
11. F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle (6th Ed.), Akadémiai Kiadó, Budapest (1972); B. Sz.-Nagy, "Unitary dilations of Hubert space operators and related topic," in: Expository Lectures from the CBMS Regional Conference Held at the University of New Hampshire, June 7-11, 1971, Amer. Math. Soc., Providence, R. I. (1974).
12. F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle (6th Ed.), Akadémiai Kiadó, Budapest (1972); B. Sz.-Nagy, "Unitary dilations of Hubert space operators and related topic," in: Expository Lectures from the CBMS Regional Conference Held at the University of New Hampshire, June 7-11, 1971, Amer. Math. Soc., Providence, R. I. (1974).
13. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge (1934).
14. V. V. Kozlov, Reg. Chaotic Dyn., 6, 235 (2001).
15. M. Kac, Probability and Related Questions in Physics [in Russian], Mir, Moscow (1951); I. Prigogine and I. Stengers, Order out of Chaos, Hienemann, London (1984).
16. M. Kac, Probability and Related Questions in Physics [in Russian], Mir, Moscow (1951); I. Prigogine and I. Stengers, Order out of Chaos, Hienemann, London (1984).
17. N. S. Krylov, Works on the Foundations of Statistical Physics [in Russian], USSR Acad. Sci. Press, Moscow (1950); English transl. (Princeton Series in Physics), Princeton Univ. Press, Princeton, N. J. (1979).
18. N. S. Krylov, Works on the Foundations of Statistical Physics [in Russian], USSR Acad. Sci. Press, Moscow (1950); English transl. (Princeton Series in Physics), Princeton Univ. Press, Princeton, N. J. (1979).