Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping(Condensed Matter and Statistical Physics)
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概要
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In the standard mapping, the resonance regions bounded by the arcs of stable and unstable manifolds of Birkhoff saddles are constructed. A resonance chain is defined as the union of the resonance regions. Using these resonance chains, (symmetric) Non-Birkhoff periodic orbits of Farey type (NBF) are introduced. With the aid of the reversibility and the structure of the stable and unstable manifolds of the fixed point and of the resonance regions, the existence of NBFs is proved, and the dynamical order relations among NBFs are derived. Finally, the relation between our results and a theorem proved by Boyland is discussed.
- 理論物理学刊行会の論文
- 2007-04-25
著者
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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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