Entropy dimension of topological dynamical systems
Entropy dimension of topological dynamical systems
We introduce the notion of topological entropy dimension to measure the complexity of entropy zero systems. It measures the superpolynomial, but subexponential, growth rate of orbits. We also introduce the dimension set, $\mathcal {D}(X,T)\subset [0,1]$, of a topological dynamical system to study the complexity of its factors. We construct a …