Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 531024, 10 pages
doi:10.1155/2009/531024
Research Article

Time-Dependent Circular Billiard

J. E. Howard

Center for Integrated Plasma Studies, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USA

Received 6 May 2009; Revised 8 July 2009; Accepted 15 July 2009

Academic Editor: Edson Denis Leonel

Copyright © 2009 J. E. Howard. 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. 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
  2. A. J. Lichtenberg and M. L. Lieberman, Regular and Chaotic Dynamics, Springer, New York, NY, USA, 1980.
  3. S. O. Kamphorst and S. P. de Carvalho, “Bounded gain of energy on the breathing circle billiard,” Nonlinearity, vol. 12, no. 5, pp. 1363–1371, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. E. Howard, A. J. Lichtenberg, M. A. Lieberman, and R. H. Cohen, “Four-dimensional mapping model for two-frequency electron cyclotron resonance heating,” Physica D, vol. 20, no. 2-3, pp. 259–284, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. E. Howard, “Theory of two-frequency microwave ionization of hydrogen atoms,” Physics Letters A, vol. 156, no. 6, pp. 286–292, 1991. View at Publisher · View at Google Scholar
  6. A. Haffmans, R. Blümel, P. M. Koch, and L. Sirko, “Prediction of a new peak in two-frequency microwave “ionization” of excited hydrogen atoms,” Physical Review Letters, vol. 73, no. 2, pp. 248–251, 1994. View at Publisher · View at Google Scholar
  7. L. Sirko, S. Yoakum, A. Haffmans, and P. M. Koch, “Microwave-driven He Rydberg atoms: Floquet-state degeneracy lifted by a second frequency, Stueckelberg oscillations, and their destruction by added noise,” Physical Review A, vol. 47, no. 2, pp. R782–R785, 1993. View at Publisher · View at Google Scholar
  8. R. Douady, “These de 3eme cycle (unpublished),” Universite Paris VII, 1982.
  9. 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 014013, 2008. View at Publisher · View at Google Scholar
  10. J. E. Howard, A. J. Lichtenberg, and M. A. Lieberman, “Two-frequency Fermi mapping,” Physica D, vol. 5, no. 2-3, pp. 243–257, 1982. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. E. Howard and S. M. Hohs, “Stochasticity and reconnection in Hamiltonian systems,” Physical Review A, vol. 29, no. 1, pp. 418–421, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. E. Howard and R. S. MacKay, “Linear stability of symplectic maps,” Journal of Mathematical Physics, vol. 28, no. 5, pp. 1036–1051, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet