Nonsymmetric Saddle-Node Pairs for the Reversible Smale Horseshoe Map(General and Mathematical Physics)
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概要
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In the reversible Smale horseshoe, we introduce a new symbol sequence other than the conventional one made of symbols 0 and 1. This system is based on subregions E, F, S, and D of resonance regions of rotation number between 0 and 1/2. We call E(p/q), F(p/q), S(p/q), and D(p/q) for 0 < p/q < 1/2, and E(1/2) and S(1/2) blocks. These blocks play the role of symbols. Thus, the number of symbols is infinite. In the system, space is divided finer and time is divided coarser. Given a periodic orbit, we want to know the origin of the orbit, that is, how the orbit has been bifurcated. In this paper, we look for the pair component of saddle-node pairs. We propose a procedure to find the pair component for a given nonsymmetric periodic orbit of the general type. If it turns out that there is no pair component, we suggest that the periodic orbit has been born through equiperiod bifurcation or period-doubling bifurcation.
- 2012-07-25
著者
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TANIKAWA Kiyotaka
National Astronomical Observatory
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Tanikawa Kiyotaka
National Astronomical Obseruatory
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Yamaguchi Yoshihiro
Teikyo Heisei Univ. Chiba Jpn
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