A remark on the smoothness of critical KAM curves in the standard mapping

Progress of Theoretical Physics

Volumn 101, Issue 1, 1999, Pages 1-24

  Yamaguchi, Yoshihiro ^a   Tanikawa, Kiyotaka ^b  

^a TEIKYO HEISEI UNIVERSITY   (Japan)

^b NATIONAL ASTRONOMICAL OBSERVATORY OF JAPAN   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033240771     PISSN: 0033068X     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTP.101.1     Document Type: Article

References (26)

1. G. B. Birkhoff, Acta Math. 43 (1920), 44.
2. M. R. Herman, Publ. Math. I. H. E. S. 49 (1979), 5.
3. J. Moser, SIAM REVIEW 28 (1986), 459.
4. S. Shinohara and Y. Aizawa, Prog. Theor. Phys. 97 (1997), 379. D. del-Castillo-Negrete, J. M. Green and P. J. Morrison, Physica D91 (1996), 1.
5. S. Shinohara and Y. Aizawa, Prog. Theor. Phys. 97 (1997), 379. D. del-Castillo-Negrete, J. M. Green and P. J. Morrison, Physica D91 (1996), 1.
6. A. Denjoy J. Math. Pures Appl. 11 (1932), 333. W. de Melo and S. van Strien, One-dimensional dynamics (Springer, 1993). See also 2).
7. A. Denjoy J. Math. Pures Appl. 11 (1932), 333. W. de Melo and S. van Strien, One-dimensional dynamics (Springer, 1993). See also 2).
8. Y. Katznelson and D. Ornstein, J. Analyse 60 (1989), 157.
9. S. Stirnemann, Commun. Math. Phys. 152 (1993), 369.
10. A. H. Osbaldestin and M. Y. Sarkis, J. of Phys. A20 (1987), L953.
11. B. R. Hunt, K. M. Khanin, Y. G. Sinai and J. A. Yorke, J. Stat. Phys. 85 (1996), 261.
12. L. E. Reichl, The transition to chaos (Springer-Verlag, 1992). R. S. Maclay, Renormalisation in area-preserving maps (World Scientific, 1993).
13. L. E. Reichl, The transition to chaos (Springer-Verlag, 1992). R. S. Maclay, Renormalisation in area-preserving maps (World Scientific, 1993).
14. R. De Vogelaere, in Contribution to the theory of nonlinear oscillation, Vol. IV, ed. S. Lefschetz (Princeton University Press, 1958), p. 53.
15. K. Tanikawa and Y. Yamaguchi, J. Math. Phys. 28 (1987), 921; 30 (1989), 608.
16. K. Tanikawa and Y. Yamaguchi, J. Math. Phys. 28 (1987), 921; 30 (1989), 608.
17. Y. H. Ichikawa, T. Kamimura, T. Hatori and S. Y. Kim, Prog. Theor. Phys. Suppl. No. 98 (1989), 1.
18. J. N. Mather, Erg. Th. Dyn. Sys. 4 (1984), 301.
19. J. Greene, J. Math. Phys. 20 (1979), 1183.
20. R. S. Mackay and I. C. Percival, Commun. Math. Phys. 98 (1985), 469.
21. I. Jungreis Erg. Th. Dyn. Sys. 11 (1991), 79.
22. S. Aubry, Physica D7 (1983), 240. J. N. Mather, Publ. Math. I. H. E. S. 63 (1986), 153.
23. S. Aubry, Physica D7 (1983), 240. J. N. Mather, Publ. Math. I. H. E. S. 63 (1986), 153.
24. S. J. Shenker and L. P. Kadanoff, J. Stat. Phys. 27 (1982), 631.
25. A. Morbidelli and A. Giorgilli, J. Stat. Phys. 78 (1994), 1607.
26. E. Lega and C. Froeschlé, Physica D 95 (1996), 97.