Open AccessOn Fractal Properties for Pre-image Entropy
Author(s) -
Teng-San Shih
Publication year - 2021
Publication title -
physical science international journal
Language(s) - English
Resource type - Journals
ISSN - 2348-0130
DOI - 10.9734/psij/2021/v25i1230300
Subject(s) - mathematics , fractal dimension , entropy (arrow of time) , subspace topology , fractal , pure mathematics , mathematical analysis , physics , quantum mechanics
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.