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Prog. Theor. Phys. Vol. 103 No. 6 (2000) pp. 1127-1136

[ Full Text PDF : FREE ACCESS (461K) ]

A Condition for the Existence of Homoclinic Intersection in C2 Standard-Like Mappings

Yoshihiro Yamaguchi1 and Kiyotaka Tanikawa2

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

(Received January 11, 2000)

Abstract:

A sufficient condition for the existence of homoclinic intersection in the doubly reversible C2 standard-like mappings is obtained. To derive the condition, we only use the geometrical structure of stable and unstable manifolds and information regarding the first and second derivatives of the mapping function. The obtained result can be applied to many mapping systems.


URL : http://ptp.ipap.jp/link?PTP/103/1127/
DOI : 10.1143/PTP.103.1127

[ Full Text PDF : FREE ACCESS (461K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 105 No. 3 (2001) pp. 399-407 :
    Running Homoclinic and Periodic Points in Standard-Like Mappings
    Kiyotaka Tanikawa and Yoshihiro Yamaguchi
  2. 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
  3. Progress of Theoretical Physics Vol. 108 No. 4 (2002) pp. 669-678 :
    Dynamical Ordering of Periodic Accelerator Modes in the Standard Mapping
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa
  4. 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
  5. 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
  6. 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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