Preimage entropy dimension of topological dynamical systems

摘要

We propose a new definition of preimage entropy dimension for continuous mapson compact metric spaces, investigate fundamental properties of the preimageentropy dimension, and compare the preimage entropy dimension with thetopological entropy dimension. The defined preimage entropy dimension holdsvarious basic properties of topological entropy dimension, for example, thepreimage entropy dimension of a subsystem is bounded by that of the originalsystem and topologically conjugated systems have the same preimage entropydimension. Also, we discuss the relation between the preimage entropy dimensionand the preimage entropy.