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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 848619, 4 pages
http://dx.doi.org/10.1155/2009/848619
Editorial

Time-Dependent Billiards

1Physics Faculty, Moscow State University, Moscow 119992, Russia
2Departamento de Estatística, Matemática Aplicada e Computação, Universidade Estadual Paulista, Avenida 24A 1515, 13506-700 Rio Claro, SP, Brazil

Received 24 August 2009; Accepted 24 August 2009

Copyright © 2009 Alexander Loskutov and Edson D. Leonel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Birkhoff, Dynamical Systems, American Mathematical Society, Providence, RI, USA, 1927.
  2. N. S. Krylov, Works on the Foundations of Statistical Physics, Princeton University Press, Princeton, NJ, USA, 1979. View at MathSciNet
  3. Ya. G. Sinai, “Dynamical systems with elastic reflections,” Russian Mathematical Surveys, vol. 25, no. 2, pp. 137–189, 1970. View at Google Scholar
  4. L. A. Bunimovich, “On the ergodic properties of certain billiards,” Functional Analysis and Its Applications, vol. 8, pp. 73–74, 1974. View at Google Scholar
  5. L. A. Bunimovich and Ya. G. Sinai, “Statistical properties of Lorentz gas with periodic configuration of scatterers,” Communications in Mathematical Physics, vol. 78, no. 4, pp. 479–497, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. Loskutov, “Dynamical chaos: systems of classical mechanics,” Physics-Uspekhi, vol. 50, no. 9, pp. 939–964, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. E. Fermi, “On the origin of the cosmic radiation,” Physical Review, vol. 75, no. 8, pp. 1169–1174, 1949. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Springer, New York, NY, USA, 1992.
  9. A. K. Karlis, P. K. Papachristou, F. K. Diakonos, V. Constantoudis, and P. Schmelcher, “Fermi acceleration in the randomized driven Lorentz gas and the Fermi-Ulam model,” Physical Review E, vol. 76, no. 1, Article ID 016214, 2007. View at Publisher · View at Google Scholar
  10. E. D. Leonel, “Breaking down the Fermi acceleration with inelastic collisions,” Journal of Physics A, vol. 40, no. 50, pp. F1077–F1083, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. E. D. Leonel and M. R. Silva, “A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration,” Journal of Physics A, vol. 41, no. 1, Article ID 015104, 13 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. Yu. Loskutov, A. B. Ryabov, and L. G. Akinshin, “Mechanism of Fermi acceleration in dispersing billiards with time-dependent boundaries,” Journal of Experimental and Theoretical Physics, vol. 89, no. 5, pp. 966–974, 1999. View at Google Scholar · View at Scopus
  13. A. Loskutov, A. B. Ryabov, and L. G. Akinshin, “Properties of some chaotic billiards with time-dependent boundaries,” Journal of Physics A, vol. 33, no. 44, pp. 7973–7986, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. E. de Carvalho, F. C. de Souza, and E. D. Leonel, “Fermi acceleration on the annular billiard,” Physical Review E, vol. 73, no. 6, Article ID 066229, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. L. P. Livorati, D. G. Ladeira, and E. D. Leonel, “Scaling investigation of Fermi acceleration on a dissipative bouncer model,” Physical Review E, vol. 78, no. 5, Article ID 056205, 2008. View at Publisher · View at Google Scholar
  16. F. Lenz, F. K. Diakonos, and P. Schmelcher, “Tunable fermi acceleration in the driven elliptical billiard,” Physical Review Letters, vol. 100, no. 1, Article ID 014103, 2008. View at Publisher · View at Google Scholar
  17. A. Loskutov and A. Ryabov, “Particle dynamics in time-dependent stadium-like billiards,” Journal of Statistical Physics, vol. 108, no. 5-6, pp. 995–1014, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. R. E. de Carvalho, F. C. de Souza, and E. D. Leonel, “Fermi acceleration on the annular billiard: a simplified version,” Journal of Physics A, vol. 39, no. 14, pp. 3561–3573, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. V. Gelfreich and D. Turaev, “Fermi acceleration in non-autonomous billiards,” Journal of Physics A, vol. 41, no. 21, Article ID 212003, 6 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. V. Gelfreich and D. Turaev, “Unbounded energy growth in Hamiltonian systems with a slowly varying parameter,” Communications in Mathematical Physics, vol. 283, no. 3, pp. 769–794, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. Loskutov, O. Chichigina, and A. Ryabov, “Thermodynamics of dispersing billiards with time-dependent boundaries,” International Journal of Bifurcation and Chaos, vol. 18, no. 9, pp. 2863–2869, 2008. View at Publisher · View at Google Scholar · View at MathSciNet