AN IMPROVEMENT OF THE BAKER’S TRANSFORMATION AND ITS EXTENSION TO HIGHER DIMENSIONS

Hirosi Sugiyama (Japan) and Juro Takezaki (Japan)

Abstract

A modified baker’s transformation is introduced: a better model of the real kneading process. As with the ordinary baker’s transformation, our modified one is also shown to be isomorphic to the Bernoulli shift, where the alternating binary expansion (Gray Code) of the coordinates of points in the unit square is used. Further, the -dimensional modified baker’s transformation is defined and is proved to be isomorphic to the m-step Bernoulli shift.

Keywords and phrases: baker’s transformation, Bernoulli shift, isomorphic.