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Prog. Theor. Phys. Vol. 114 No. 4 (2005) pp. 763-791

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Generalized Dynamical Ordering and Topological Entropy in the Hénon Map

Yoshihiro Yamaguchi1 and Kiyotaka Tanikawa2

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

(Received May 11, 2005)

Abstract:

Under area- and orientation-preserving maps, the images of the symmetry axes accumulate at the unstable manifold of a saddle fixed point P, while their inverse images accumulate at the stable manifold of P. Before or after the tangency of these stable and unstable manifolds, four types of generalized dynamical ordering are derived. They determine the order of the appearance of the symmetric periodic orbits. We derive these types of ordering for the area- and orientation-preserving Hénon map. A lower bound of the topological entropy is obtained by using the symbol sequence of the periodic orbits included in the dynamical ordering and the trellis method.


URL : http://ptp.ipap.jp/link?PTP/114/763/
DOI : 10.1143/PTP.114.763

[ Full Text PDF : FREE ACCESS (810K) ] Citation:

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Citing Article(s) :

  1. 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
  2. Progress of Theoretical Physics Vol. 116 No. 6 (2006) pp. 1029-1049 :
    Order of Appearance of Homoclinic Points for the Hénon Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  3. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 657-669 :
    Topological Entropy in a Parameter Range of the Standard Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  4. Progress of Theoretical Physics Vol. 122 No. 3 (2009) pp. 569-609 :
    A New Interpretation of the Symbolic Codes for the Hénon Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  5. Progress of Theoretical Physics Vol. 126 No. 5 (2011) pp. 811-839 :
    Forcing Relations for Homoclinic Orbits of the Reversible Horseshoe Map
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa

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