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

本研究的目的是在观测到周期约为几百天的Mira、半规则型和不规则型恒星等长周期变量的光曲线的基础上，探讨晚型巨脉动变量的不规则光变化是否可以理解为混沌行为。为了获得分析的基础数据，我对长周期变量进行了光度观测，并打算制作数据库，收集了日本过去未发表的这些恒星的目视观测数据。为了与长周期变量进行比较，我还观测了ZZ Psc，这是一颗脉动白矮星，它的周期非常短，大约为1000秒。光度观测是在国家天文台的Dodaira站和数据库进行的，该数据库有大约100万次对大约5000颗恒星的观测，包括从1910年早期到现在的长周期变量。现在，已经完成了。由于这个数据库将对变星的各种研究非常有用，我打算向研究人员开放。利用以上获得的数据，我通过周期分析、制作首回图、相关积分等方法，对一些数据充足的Mira和半规则星进行了统计和动态分析，发现了混沌。结果如下：尽管在Mira和半规则恒星中进行了多次寻找混沌的试验，但似乎无法找到混沌的严格证据。但是，如果光曲线是混沌的，则半规则恒星的尺寸比Miras大。从第一次返回的地图来看，与其他光谱类型相比，碳星显示出独特的特征。对于ZZ Psc，我也找不到混沌，但发现了周期变化。

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I carried out photometric observations for long period variables and intended to make database, which collected unpublished visual observations for these stars in Japan in the past.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.