Entropy and ergodicity of boole-type transformations
Authors:
- Denis Blackmore,
- Alexander A. Balinsky,
- Radosław Kycia,
- Anatolij K. Prykarpatski
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.
- Record ID
- CUT9758280ac5014925ae7f8c6f73995507
- Publication categories
- ;
- Author
- Journal series
- Entropy, ISSN , e-ISSN 1099-4300, Monthly
- Issue year
- 2021
- Vol
- 23
- No
- 11
- Pages
- [1-22]
- Article number
- 1405
- Other elements of collation
- Bibliografia (na s.) - 20-22; Bibliografia (liczba pozycji) - 77; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 23, Iss. 11, Spec. Iss.
- Substantive notes
- Special Issue: Aspects of Topological Entropy
- Keywords in English
- discrete transformations, invariant measure, ergodicity, entropy, Bernoulli type transformations, Boole-type transformations, fibered multidimensional mappings, induced transformations
- DOI
- DOI:10.3390/ e23111405 Opening in a new tab
- URL
- https://www.mdpi.com/1099-4300/23/11/1405 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 100
- Publication indicators
- = 3
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT9758280ac5014925ae7f8c6f73995507/
- URN
urn:pkr-prod:CUT9758280ac5014925ae7f8c6f73995507
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.