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Siberian Mathematical Journal

, Volume 46, Issue 2, pp 260–269 | Cite as

One-dimensional motion of N balls

  • R. M. Garipov
Article
  • 22 Downloads

Abstract

We find all elastic systems with point spectrum. For almost elastic nonconservative systems we obtain large time asymptotics for the velocities of the balls. This one-dimensional ball model was invoked in order to elucidate some problems of gas kinetics and turbulence but turned out hard to study in its own right.

Keywords

dynamical system crystallographic group factorization point spectrum small nonconservativity average velocity fluctuation 

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References

  1. 1.
    Garipov R. M., “One-dimensional motion of rigid balls,” Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 6, 181 (1974).Google Scholar
  2. 2.
    Kornfel’d I. P., Sina \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Ya. G.,and Fomin S. V., Ergodic Theory [in Russian], Nauka, Moscow (1980).Google Scholar
  3. 3.
    Garipov R. M. and Mamontov E. V., “One-dimensional motion of inelastic balls. I: Reduction to discrete time,” Sibirsk. Mat. Zh., 34, No.6, 23–33 (1993).Google Scholar
  4. 4.
    Garipov R. M. and Mamontov E. V., “One-dimensional motion of inelastic balls. II: 2-Tied quasicycles,” Sibirsk. Mat. Zh., 35, No.5, 1006–1025 (1994).Google Scholar
  5. 5.
    Ratcliffe J. G., Foundations of Hyperbolic Manifolds Springer-Verlag, New York; Berlin (1994). (Graduate Texts in Math.; 149.)Google Scholar
  6. 6.
    Garipov R. M., An Algebraic Method for Calculating Crystallographic Groups and the X-Ray Structure Analysis of Crystals [in Russian], Novosibirsk Univ., Novosibirsk (2003).Google Scholar
  7. 7.
    Bourbaki N., Lie Groups and Algebras [Russian translation], Mir, Moscow (1972).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • R. M. Garipov
    • 1
  1. 1.Lavrent’ev Institute of HydrodynamicsNovosibirsk

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