New Period-Doubling and Equiperiod Bifurcations of the Reversible Area-Preserving Map(General and Mathematical Physics)
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概要
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Two types of period-doubling and equiperiod bifurcations of the reversible area-preserving map are studied. Ordinary period-doubling bifurcation means that the eigenvalue of the mother elliptic periodic orbit (u) is -1, u becomes a saddle periodic orbit with reflection, and an elliptic daughter periodic orbit (v) appears, where the period of v is twice that of u. The other period-doubling bifurcation named the reverse period-doubling bifurcation means that the eigenvalue of the mother saddle periodic orbit with reflection (u') is -1, u' becomes an elliptic orbit, and a daughter periodic orbit (v') appears, where the period of v' is twice that of u'. The daughter periodic orbit is a saddle with reflection. We prove that both the daughters v and v' exist in the reversible Smale horseshoe. The forcing relation of the ordinary and reverse period-bifurcations is obtained. Similarly, the ordinary equiperiod and reverse equiperiod bifurcations are also discussed.
- 2012-11-25
著者
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YAMAGUCHI Yoshihiro
Teikyo Heisei University
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Tanikawa Kiyotaka
National Astronomical Obseruatory
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Yamaguchi Yoshihiro
Teikyo Heisei Univ. Chiba Jpn
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