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

本研究的目的是为了探讨晚型巨型脉动变星的不规则光变化是否可以理解为混沌行为，并根据周期约为几百天的长周期变星(包括MIRA、半规则和不规则型恒星)的观测光曲线。为了获得分析所需的基础数据，我进行了长周期变星的光度观测，并打算建立数据库，收集过去日本对这些恒星的未发表的目测数据。为了与长周期变星进行比较，我还观测了一颗脉动白矮星ZZ PSC，它的周期很大，约为1000秒。国家天文台Dodaira站和数据库进行了光度观测，其中包括从1910年初至S的约5000颗恒星的约100万次观测。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，我打算向研究人员敞开大门。利用上述获得的数据，我通过周期分析、制作一次回归图、相关积分等方法，对一些有足够数据的米拉和半正则星进行了统计和动力学分析，发现了一些米拉和半正则星的混沌。结果如下：尽管人们多次尝试寻找米拉和半正则星的混沌，但似乎找不到严格的混沌证据。然而，如果光曲线是混沌的，则半规则恒星的维度比水星大。从首次返回图上看，碳星与其他光谱类型相比显示出独特的特征。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I carried out photometric observations for long period variables and intended to make database, which collected unpublished visual observations for these stars in Japan in the past.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.