Exhaustive weakly wandering sequences for alpha type transformations

• Online Access: http://hdl.handle.net/2047/d20000069

In this thesis, new conditions are given which allow for the control of the exhaustive weakly wandering sequence of an ergodic, infinite measure preserving transformation. It is also shown how to control the 캱-type of a transformation. These are then extended to permit the simultaneous control of both the exhaustive weakly wandering sequence and the α-type. Applying these results, new transformations are presented. The first known examples are given of 0-type and 1/3-type with known exhaustive weakly wandering sequences. In addition, we present an explicit sequence of integers which is exhaustive weakly wandering for α-type transformations of every α ∈ [0,1]. This is the first known example of an exhaustive weakly wandering sequence which works for more than one α-type.