called compound states are realized.

We now have understood the both ends of these processes: The frequency of the giant resonance, for instance, can be well evaluated by the random phase approximation (RPA). Compound states, on the other hand, are also well described by the random matrix theory with the Gaussian orthogonal ensemble (GOE) [@dyson; @mehta], which characterizes a classical chaotic motion.

It is still not well understood, however, how the dynamics changes from regular to chaotic [@mottelson]. In order to answer this question, it is very useful to study the fluctuation properties of the strength functions: The structure at the large energy scale of the strength function corresponds to the behavior of the initial stage, while the fluctuation properties at small energy scale correspond to the long time behavior.

We proposed and have used a novel fluctuation analysis based on the quantity we call the local scaling dimension to study the fluctuation properties of the strength functions [@aiba]. This method is devised to quantitatively characterize the fluctuation at each energy scale, and is suitable for the investigation of the fine structure of the strength function.

The strength distribution of giant resonances and its fluctuation have also been studied experimentally. 