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Prog. Theor. Phys. Vol. 104 No. 5 (2000) pp. 943-954

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Symmetrical Non-Birkhoff Period-3 Orbits in Standard-Like Mappings

Yoshihiro Yamaguchi1 and Kiyotaka Tanikawa2

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

(Received June 22, 2000)

Abstract:

A necessary condition for the existence of non-Birkhoff period-3 orbits is derived in C0 standard-like mappings. Symmetrical non-Birkhoff period-3 orbits of the pseudo-Anosov braid-type are found. In this case, the standard-like mapping is a pseudo-Anosov system in a certain parameter range. The braid types of all period-3 orbits are derived. Using these braids, a lower bound of the topological entropy is obtained. These orbits do not exist in a horseshoe.


URL : http://ptp.ipap.jp/link?PTP/104/943/
DOI : 10.1143/PTP.104.943

[ Full Text PDF : FREE ACCESS (490K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 106 No. 4 (2001) pp. 691-696 :
    Non-Symmetric Non-Birkhoff Period-2 Orbits in the Standard Mapping
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  2. Progress of Theoretical Physics Vol. 106 No. 6 (2001) pp. 1097-1114 :
    Dynamical Ordering of Non-Birkhoff Periodic Orbits in a Forced Pendulum
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  3. 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
  4. Progress of Theoretical Physics Vol. 108 No. 6 (2002) pp. 987-997 :
    Non-Symmetric Periodic Points in Reversible Maps
    Kiyotaka Tanikawa and Yoshihiro Yamaguchi
  5. 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
  6. Progress of Theoretical Physics Vol. 113 No. 2 (2005) pp. 261-281 :
    Generalized Horseshoes in the Standard Mapping
    Kiyotoka Tanikawa and Yoshihiro Yamaguchi
  7. 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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