A New Interpretation of the Symbolic Codes for the Henon Map(General and Mathematical Physics)
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概要
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After the completion of the horseshoe for the Henon map, periodic orbits and homoclinic orbits are characterized by the symbolic code represented by 0's and 1's. Seven problems for these codes are proposed. The resonance regions are constructed using the stable and unstable manifolds of saddle points appearing through the rotational bifurcation of the elliptic fixed point. On the basis of the concept of resonance regions, the code is separated into several blocks. Separated blocks are represented by new four block words. Thus, all periodic orbits and homoclinic orbits are represented by these codes. On the basis of the concept of block structure, we obtain the complete or partial answers or the conjecture to these problems.
- 2009-09-25
著者
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YAMAGUCHI Yoshihiro
Teikyo Heisei University
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TANIKAWA Kiyotaka
National Astronomical Observatory
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Yamaguchi Yoshihiro
Teikyo Heisei Univ. Tokyo Jpn
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Tanikawa Kiyotaka
National Astronomical Obseruatory
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Yamaguchi Yoshihiro
Teikyo Heisei Univ. Chiba Jpn
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