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TMF, 2003, Volume 136, Number 3, Pages 496–506 (Mi tmf1914)  

This article is cited in 9 scientific papers (total in 9 papers)

Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems

V. V. Kozlov, D. V. Treschev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We establish the existence of weak limits of solutions (in the class $L_p$, $p\ge1$) of the Liouville equation for nondegenerate quasihomogeneous Hamilton equations. We find the limit probability distributions in the configuration space. We give conditions for a uniform distribution of Gibbs ensembles for geodesic flows on compact manifolds.

Keywords: quasihomogeneous Hamiltonian system, geodesic flow, weak limit, Gibbs ensemble, uniform distribution

DOI: https://doi.org/10.4213/tmf1914

Full text: PDF file (264 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 136:3, 1325–1335

Bibliographic databases:

Received: 17.12.2002
Revised: 21.04.2003

Citation: V. V. Kozlov, D. V. Treschev, “Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems”, TMF, 136:3 (2003), 496–506; Theoret. and Math. Phys., 136:3 (2003), 1325–1335

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kozlov VV, “Billiards, invariant measures, and equilibrium thermodynamics - II”, Regular & Chaotic Dynamics, 9:2 (2004), 91–100  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. V. V. Kozlov, D. V. Treschev, “Fine-grained and coarse-grained entropy in problems of statistical mechanics”, Theoret. and Math. Phys., 151:1 (2007), 539–555  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Bogachev, VI, “On the ergodic theorem in the Kozlov-Treshchev form”, Doklady Mathematics, 75:1 (2007), 47  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Kozlov, VV, “Gibbs ensembles, equidistribution of the energy of sympathetic oscillators and statistical models of thermostat”, Regular & Chaotic Dynamics, 13:3 (2008), 141  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Kozlov V.V., “Vorticity equation of 2D-hydrodynamics, Vlasov steady-state kinetic equation and developed turbulence”, Iutam Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Iutam Bookseries, 6, 2008, 27–37  crossref  mathscinet  zmath  isi
    6. A. V. Korolev, “On the Convergence of Nonuniform Ergodic Means”, Math. Notes, 87:6 (2010), 912–915  mathnet  crossref  crossref  mathscinet  isi
    7. Korolev A.V., “On the Ergodic Theorem in the Kozlov-Treshchev Form for An Operator Semigroup”, Ukrainian Math J, 62:5 (2010), 809–815  crossref  zmath  isi  elib  scopus  scopus
    8. Bogachev V.I., Korolev A.V., Pilipenko A.Yu., “Non Uniform Averagings in the Ergodic Theorem for Stochastic Flows”, Doklady Mathematics, 81:3 (2010), 422–425  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Trushechkin A., “Microscopic and Soliton-Like Solutions of the Boltzmann Enskog and Generalized Enskog Equations For Elastic and Inelastic Hard Spheres”, Kinet. Relat. Mod., 7:4 (2014), 755–778  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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