Distorted Histories: Mathematical Histories Distorted by Certain Mathematical Objects

The main purpose of this monograph is to show the existence of distortions of histories, and analyze the distorted histories in operator-algebraic points of view. We provide two types of distortions occured by some finite number of objects. In dynamical systems, we define a history by a pair, consisting of a type I factor, and an E_0-group with some additional conditions. We distort the given history by a finite number of partial isometries. Two types of distortions can happen: inner distortions, and outer distortions. The fundamental properties of distorted histories are characterized. We also study the operator algebras generated by distorted histories. Also, by comparing operator algebras generated by histories and those generated by distorted histories, we investigate the differences between them. As application, we observe the fractally distorted histories, which are one type of the ``patterned'' distorted histories.