Generalized horseshoes in the standard mapping

Progress of Theoretical Physics

Volumn 113, Issue 2, 2005, Pages 261-281

  Tanikawa, Kiyotoka ^a   Yamaguchi, Yoshihiro ^b  

^a NATIONAL ASTRONOMICAL OBSERVATORY OF JAPAN   (Japan)

^b TEIKYO HEISEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18444372939     PISSN: 0033068X     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTP.113.261     Document Type: Article

References (24)

1. S. Smale, Bull. Am. Math. Soc. 73 (1967), 747.
2. S. Wiggins, Chaotic Transport in Dynamical Systems (Springer-Verlag, 1991).
3. M. Hénon, Commun. Math. Phys. 50 (1976), 69.
4. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, 1983).
5. F. A. McRobie and J. M. T. Thompson, Dynam. Stab. Sys. 9 (1994), 223.
6. C. Jung, C. Mejia-Monasterio, O. Merlo and T. H. Seligman, New J. Phys. 6 (2004), 48.
7. P. Gaspard, Chaos, scattering and statistical mechanics (Cambridge University Press, 1998).
8. P. Collins, Int. J. Bifurcation and Chaos 12 (2002), 605.
9. See also "Dynamics of surface maps with homoclinic and heteroclinic tangles", Ph. D thesis (University of California, Berkeley, 1999).
10. Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. 104 (2000), 943.
11. Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. 106 (2001), 691.
12. Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. 107 (2002), 1117.
13. Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. 110 (2003), 861.
14. T. Matsuoka, in Dynamical System 1 (World Scientific, 1986), p. 58;
15. Contemp. Math. 152 (1993), 229.
16. See also Bussei Kenkyu 67 (Kyoto) (1996), 1.
17. R. De Vogelaere, in Contributions to the Theory of Oscillations, Vol. IV, Ann. Math. Studies No. 41 (Princeton University Press, 1958).
18. V. F. Lazutkin, I. G. Schachmannski and M. B. Tabanov, Physica D 40 (1989), 235.
19. K. Tanikawa and Y. Yamaguchi, Chaos 12 (2002), 33.
20. Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. 111 (2004), 689.
21. M. Bestvina and M. Handel, Ann. Math. 135 (1992), 1.
22. D. Lind and B. Marcus, An introduction to Symbolic Dynamics and Coding (Cambridge University Press, 1995).
23. K. Tanikawa and Y. Yamaguchi, J. Math. Phys. 30 (1989), 608.
24. J. Palis, Topology 8 (1969), 385.