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Prog. Theor. Phys. Vol. 106 No. 6 (2001) pp. 1097-1114

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Dynamical Ordering of Non-Birkhoff Periodic Orbits in a Forced Pendulum

Yoshihiro Yamaguchi1 and Kiyotaka Tanikawa2

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

(Received August 8, 2001)

Abstract:

Forced pendulums induce reversible non-monotone twist mappings. Non-Birkhoff periodic orbits (NBO) are found in these mappings, and hence in the pendulums. The existence of an NBO is equivalent to the non-integrability of the system. Two types of dynamical ordering for NBOs are obtained.


URL : http://ptp.ipap.jp/link?PTP/106/1097/
DOI : 10.1143/PTP.106.1097

[ Full Text PDF : FREE ACCESS (724K) ] Citation:

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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. 108 No. 2 (2002) pp. 231-240 :
    Non-Birkhoff Periodic Orbits in a Circle Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  3. 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
  4. Progress of Theoretical Physics Vol. 110 No. 5 (2003) pp. 861-874 :
    Topological Entropy in a Forced Duffing System
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa

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