9804994 Johnson The objective of this research by Aimee Johnson is to investigate loosely Bernoulli Z^d dynamical systems. This work will build on the result of D. Ornstein which states that weakly Bernoulli systems can be completely characterized, up to isomorphism, by their entropy. Ornstein's result uses the d-bar-metric, and Ornstein, D. Rudolph, and B. weiss characterize the classification theory brought about when this is replaced with the f-bar-metric. Their work involves 1-dimensional actions and the purpose of this research is to generalize these results to higher dimensions. In particular, one objective is to show that higher dimensional loosely Bernoulli systems are the distinguished class for the higher dimensional version of even Kakutani equivalence, which is known to be true in 1-dimension. This equivalence theory will be useful in investigating properties of general dynamical systems. Johnson has already worked in this area in joint work with Ayse Sahin, giving a zero entropy definition of loosely Bernoulli and developing technical lemmas which have proven to be helpful in showing when a system is loosely Bernoulli. Another objective of this research is to provide more examples of loosely Bernoulli systems, thus increasing the accessibility of this field.
