Removal of resonances by rotation in linearly degenerate two-dimensional oscillator systems

Journal of Mathematical Physics

Volumn 48, Issue 4, 2007, Pages

  Khasin, Michael ^a   Friedland, Lazar ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247576410     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2719145     Document Type: Article

References (23)

1. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin, 1974).
2. R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavski, Nonlinear Physics: From Pendulum to Turbulence and Chaos (Harwood Academic Press, New York, 1988).
3. J. Fajans and L. Friedland, Am. J. Phys. 0002-9505 10.1119/1.1389278 69, 1096 (2001).
4. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980).
5. A. M. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras (Birkhäuser Verlag, Berlin, 1990).
6. F. G. Gustavson, Astron. J. 0004-6256 10.1086/110172 71, 670 (1966).
7. F. Verhulst, in Symmetry and Perturbation Theory, edited by, D. Bambusi, and, G. Gaeta, (Quaderni GNFM, Firenze, 1998).
8. H. Poincar̀, Les M̀thodes Nouvelles de la M̀canique C̀leste (Gauthier-Villars, Paris, 1892).
9. H. Von Zeipel, Ark. Mat., Astron. Fys. 11, 1 (1916).
10. M. Henon and C. Heiles, Astron. J. 0004-6256 10.1086/109234 69, 73 (1964).
11. M. Toda, Theory of Nonlinear Lattices (Springer, New York, 1981).
12. M. Lakshmanan and R. Sahadevan, Phys. Rep. 0370-1573 10.1016/0370- 1573(93)90081-N 224, 1 (1993).
13. T. Bountis, H. Segur, and F. Vivaldi, Phys. Rev. A 1050-2947 10.1103/PhysRevA.25.1257 25, 1257 (1982).
14. Y. F. Chang, M. Tabor, and J. Weiss, J. Math. Phys. 0022-2488 10.1063/1.525389 23, 531 (1982).
15. B. Dorizzi, B. Grammaticos, A. Ramani, and P. Winternitz, J. Math. Phys. 0022-2488 10.1063/1.526685 26, 3070 (1985).
16. L. D. Landau and E. M. Lifshitz, Mechanics, Course of Theoretical Physics (Pergamon Press, Oxford, 1976), Vol. 1.
17. M. J. Ablowitz, A. Ramani, and H. Segur, Lett. Nuovo Cimento Soc. Ital. Fis. 23, 333 (1978).
18. M. J. Ablowitz, A. Ramani, and H. Segur, J. Math. Phys. 0022-2488 10.1063/1.524491 21, 715 (1980).
19. Wolfram Research Inc., Mathematica 4 (Wolfram Research Inc., Champaign, IL, 1999). See EPAPS Document No. E-JMAPAQ-48-005704 for the MATHEMATICA code used in the calculations. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
20. Wolfram Research Inc., Mathematica 4 (Wolfram Research Inc., Champaign, IL, 1999). See EPAPS Document No. E-JMAPAQ-48-005704 for the MATHEMATICA code used in the calculations. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
21. R. Sahadevan, Painlev́ Analysis and Integrability of Certain Coupled Nonlinear Oscillators., Ph.D. thesis, University of Madras (1987).
22. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, 2nd ed. (Springer-Verlag, New York, 1992).
23. M. Khasin and L. Friedland, Phys. Rev. E 1063-651X 10.1103/PhysRevE.68. 066214 68, 066214 (2003).