Entropy of Baker’s Transformation

Four theorems about four different kinds of entropies for Baker’s transformation are presented. The Kolmogorov entropy of Baker’s transformation is sensitive to the initial flips by the time. The topological entropy of Baker’s transformation is found to be logk. The conditions for the state of Baker’s transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.