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Prog. Theor. Phys. Vol. 108 No. 2 (2002) pp. 231-240

[ Full Text PDF : FREE ACCESS (338K) ]

Non-Birkhoff Periodic Orbits in a Circle Map

Yoshihiro Yamaguchi1 and Kiyotaka Tanikawa2

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

(Received March 28, 2002)

Abstract:

Birkhoff and non-Birkhoff types of periodic orbits are defined in circle maps. The dynamical order relation of non-Birkhoff periodic orbits (NBOs) with period longer than or equal to three is proved. Braids are constructed for NBOs, and a lower bound for the topological entropy is derived.


URL : http://ptp.ipap.jp/link?PTP/108/231/
DOI : 10.1143/PTP.108.231

[ Full Text PDF : FREE ACCESS (338K) ] Citation:

References:

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Citing Article(s) :

  1. 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
  2. Progress of Theoretical Physics Vol. 110 No. 5 (2003) pp. 861-874 :
    Topological Entropy in a Forced Duffing System
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  3. Progress of Theoretical Physics Vol. 113 No. 5 (2005) pp. 935-951 :
    Dynamical Ordering of Symmetric Periodic Orbits for the Area Preserving Hénon Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa

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