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Prog. Theor. Phys. Vol. 113 No. 2 (2005) pp. 261-281

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Generalized Horseshoes in the Standard Mapping

Kiyotoka Tanikawa1 and Yoshihiro Yamaguchi2

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

(Received October 1, 2004)

Abstract:

There exist (2n+1)-fold horseshoes with topological entropy ln (2n+1) for n ≥1 in the standard mapping for appropriate parameter values. These generalized horseshoes form the hierarchical structure in the phase space. The dynamical order relation among the doubly reversible periodic orbits appearing through a saddle node bifurcation included in the (2n+1)-fold horseshoe is obtained.


URL : http://ptp.ipap.jp/link?PTP/113/261/
DOI : 10.1143/PTP.113.261

[ Full Text PDF : FREE ACCESS (740K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 114 No. 6 (2005) pp. 1163-1177 :
    Symmetric Periodic Orbits and Topological Entropy in the Two-Dimensional Cubic Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  2. Progress of Theoretical Physics Vol. 116 No. 5 (2006) pp. 803-817 :
    Increase of Topological Entropy until the Three-Fold Horseshoe is Completed
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa

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