On Mather's Connecting Orbits in Standard Mapping(Condensed Matter and Statistical Physics)
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概要
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Mather's connecting theorem is proved with the elementary geometrical method essentially using the reversibility of the standard mapping instead of the variational method. In the proof of the existence of orbits connecting quasi-periodic orbits of the same rotation number, non-monotonic quasi-periodic orbits (NMQs) are found, in which almost all orbital points are located in the gap of the Aubry-Mather set. The dynamical order relations among NMQs are derived. The existence of orbits connecting orbits of different irrational rotation numbers is proved using also non-Birkhoff periodic orbits of the Farey type. As an application of our method, a partial proof of Greene's criterion is given.
- 理論物理学刊行会の論文
- 2008-04-25
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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