On Feldman–Katok metric and entropy formulas

Abstract

In this paper, we study the Feldman–Katok metric and give corresponding entropy formulas by replacing Bowen metric with Feldman–Katok metric. It turns out that the Feldman–Katok metric is the weakest one, in the sense of allowing desynchrony and jump in the process of measuring orbit segments’ distance, that makes the entropy formulas valid. Some related topics are also discussed.