A Search for Chaotic Behavior in Visual Light Curves of Late Type Giant Pulsating Variables.

本项研究的目的是根据对Mira、半规则星和不规则星等周期在几百天左右的长周期变星的光变观测，探讨晚型巨星脉动变星的不规则光变是否可以理解为混沌行为，为分析提供基础数据。我对长周期变星进行了测光观测，并打算建立数据库，收集过去在日本对这些恒星的未发表的视觉观测。为了与长周期变星进行比较，我还观测了周期很小的白色矮星ZZ Psc，它的周期大约为1000秒。现在，已经完成了。由于这个数据库对变星的各种研究都很有用，所以我打算向广大研究人员开放，利用上述获得的数据，我对一些有足够数据的Mira星和半规则星，用周期分析、制作初回图、相关积分等方法，进行了统计和动力学分析，发现了混沌，结果如下：尽管人们在米拉星和半规则星中进行了许多探索混沌的尝试，但似乎找不到混沌存在的严格证据。然而，如果光变曲线是混沌的，那么半规则星的尺寸比Miras大。从第一次返回图中可以看出，碳星与其他光谱类型相比具有一些特殊的特征。对于ZZ Psc，我也找不到混沌，但找到了周期变化。

The aim of this research is to investigate, whether irregular light variations of late type giant pulsating variables can be understood as chaotic behaviour or not, oh the basis of observed light curves of long period variables including Mira, semiregular and irregular type stars, whose periods are about several hundred days.In order to get basic data for analysis, I carried out photometric observations for long period variables and intended to make database, which collected unpublished visual observations for these stars in Japan in the past. To compare with long period variables, I also observed ZZ Psc, one of the pulsating white dwarf stars, whose period is very sort and about 1000 second.Photometric observations are made at Dodaira station of National observatory and the database, which has about one million observations for about five thousand stars including long period variables from early 1910's to. the present, is completed. Since this database will be very useful to various study on variable stars, I intend to open wide to the researchers.Using the data acquired as above, I made analyses statistically and dynamically to find chaos for some Mira and semiregular stars, which have enough data, by the methods of period analysis, making first-return maps, correlation integral and so on.The results are as follows : In spite of many trials to search chaos in Mira and semiregular stars, it seems that the strict evidence of chaos cannot find. However, if the light curves are chaotic, the dimension of semiregular stars is larger than Miras. From the first-return maps, carbon stars show peculiar features compared with other spectrum types. For ZZ Psc, I cannot find chaos, too, but find period variations.