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Prog. Theor. Phys. Vol. 106 No. 4 (2001) pp. 691-696

[ Full Text PDF : FREE ACCESS (146K) ]

Non-Symmetric Non-Birkhoff Period-2 Orbits in the Standard Mapping

Yoshihiro Yamaguchi1 and Kiyotaka Tanikawa2

1Teikyo Heisei University, Ichihara 290-0193, Japan
2National Astronomical Observatory, Mitaka 181-8588, Japan

(Received June 22, 2001)

Abstract:

Period-2 badly ordered orbits (non-Birkhoff orbits) are studied in the standard mapping. Points of symmetric non-Birkhoff orbits appear on symmetry axes due to the saddle-node bifurcation, and non-symmetric non-Birkhoff orbits appear due to the equi-period bifurcation of symmetric non-Birkhoff orbits. The braids of symmetric non-Birkhoff orbits are constructed, and the topological entropy is estimated.


URL : http://ptp.ipap.jp/link?PTP/106/691/
DOI : 10.1143/PTP.106.691

[ Full Text PDF : FREE ACCESS (146K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 107 No. 6 (2002) pp. 1117-1145 :
    Dynamical Ordering of Non-Birkhoff Orbits and Topological Entropy in the Standard Mapping
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  2. Progress of Theoretical Physics Vol. 109 No. 2 (2003) pp. 187-202 :
    Non-Birkhoff Orbits with 2n Turning Points in the Standard Map
    Kiyotaka Tanikawa and Yoshihiro Yamaguchi
  3. Progress of Theoretical Physics Vol. 113 No. 2 (2005) pp. 261-281 :
    Generalized Horseshoes in the Standard Mapping
    Kiyotoka Tanikawa and Yoshihiro Yamaguchi
  4. Progress of Theoretical Physics Vol. 117 No. 4 (2007) pp. 601-632 :
    Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa

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