Folding and Metric Entropies for Extended Shifts

Abstract

In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $({\Sigma }_{m_{-},m_{+}},{\sigma }_{\varphi })$ which generalizes the standard bilateral Bernoulli shifts. The space ${\Sigma }_{m_{-},m_{+}}$ consists of symbolic sequences over two distinct finite alphabets, with dynamics governed by a shift map ${\sigma }_{\varphi }$ incorporating a non-invertible function $\varphi$ that maps one of the alphabets to the other one. These systems are, for instance, particularly useful for encoding the many-to-one baker's transformation endomorphisms, and they can also be seen as a skew product with a unilateral Bernoulli shift on the base.

References in corpus (1)

• Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows