On Fractal Properties for Pre-image Entropy
Physical Science International Journal · pp. 28–42 · Published 30 Dec 2021
10.9734/psij/2021/v25i1230300Abstract
Fractal dimension for pre-image entropy is introduced for continuous maps throughout this paper. First we show the definition of pre-image entropy dimension of a dynamical system from different topological versions. Then we give those basic propositions of pre-image entropy dimension and the formula for power inequality and forward generator. Relationships among different types of pre-image entropy dimension are studied and an inequality relating them is given. Some basic examples are provided to compare those values of polynomial growth type with the pre-image entropy dimension. After that, this study constructs a symbolic subspace to attain any value between 0 and 1 for pre-image entropy dimension.
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