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Prog. Theor. Phys. Vol. 101 No. 1 (1999) pp. 1-24

[ Full Text PDF : FREE ACCESS (302K) ]

A Remark on the Smoothness of Critical KAM Curves in the Standard Mapping

Yoshihiro Yamaguchi *) and Kiyotaka Tanikawa *,**)

Teikyo Heisei University, Ichihara 290-0193, Japan
*National Astronomical Observatory, Mitaka 181-8588, Japan

(Received October 6, 1998)

Abstract:

The smoothness of KAM (Kolmogorov-Arnold-Moser) curves when approaching the critical point which constitutes the existence/non-existence boundary of a KAM curve is investigated in the standard mapping as a typical example of analytical twist mappings. We give numerical results indicating that the KAM curve at the critical point is C1, but its derivative is not a function of bounded variation. The fractal distribution function of mapped points on such KAM curves is caused by this unbounded variation.


URL : http://ptp.ipap.jp/link?PTP/101/1/
DOI : 10.1143/PTP.101.1


*)E-mail: yy-chaos@jb3.so-net.ne.jp
**)E-mail: tanikawa@cc.nao.ac.jp

[ Full Text PDF : FREE ACCESS (302K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 103 No. 6 (2000) pp. 1127-1136 :
    A Condition for the Existence of Homoclinic Intersection in C2 Standard-Like Mappings
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  2. Progress of Theoretical Physics Vol. 104 No. 5 (2000) pp. 943-954 :
    Symmetrical Non-Birkhoff Period-3 Orbits in Standard-Like Mappings
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  3. Progress of Theoretical Physics Vol. 105 No. 3 (2001) pp. 399-407 :
    Running Homoclinic and Periodic Points in Standard-Like Mappings
    Kiyotaka Tanikawa and Yoshihiro Yamaguchi

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