Entropy and ergodicity of boole-type transformations
Document Type
Article
Publication Date
11-1-2021
Abstract
We review some analytic, measure-theoretic and topological techniques for studying ergodicity and entropy of discrete dynamical systems, with a focus on Boole-type transformations and their generalizations. In particular, we present a new proof of the ergodicity of the 1-dimensional Boole map and prove that a certain 2-dimensional generalization is also ergodic. Moreover, we compute and demonstrate the equivalence of metric and topological entropies of the 1-dimensional Boole map employing “compactified”representations and well-known formulas. Several examples are included to illustrate the results. We also introduce new multidimensional Boole-type transformations invariant with respect to higher dimensional Lebesgue measures and investigate their ergodicity and metric and topological entropies.
Identifier
85118371545 (Scopus)
Publication Title
Entropy
External Full Text Location
https://doi.org/10.3390/e23111405
e-ISSN
10994300
Issue
11
Volume
23
Recommended Citation
Blackmore, Denis; Balinsky, Alexander A.; Kycia, Radoslaw; and Prykarpatski, Anatolij K., "Entropy and ergodicity of boole-type transformations" (2021). Faculty Publications. 3703.
https://digitalcommons.njit.edu/fac_pubs/3703
