Topological entropy dimension on subsets for nonautonomous dynamical systems

Abstract

The topological entropy dimension is mainly used to distinguish the zero topological entropy systems. Two types of topological entropy dimensions, the classical entropy dimension and the Pesin entropy dimension, are investigated for nonautonomous dynamical systems. Several properties of the entropy dimensions are discussed, such as the power rule, monotonicity and equiconjugacy et al. The Pesin entropy dimension is also proved to be invariant up to equiconjugacy. The relationship between these two types of entropy dimension is also discussed in more detail. It's proved that these two entropy dimensions coincide and are equal to one provided that the classical topological entropy is positive and finite.