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@article{2227819,
author = {Blackmore, Denis and Balinsky, Alexander A and Kycia, Radoslaw Antoni and Prykarpatski, Anatolij K},
article_location = {Basel (Schwitzerland)},
article_number = {11},
doi = {http://dx.doi.org/10.3390/e23111405},
keywords = {discrete transformations; invariant measure; ergodicity; entropy; Bernoulli type transformations; Boole-type transformations; fibered multidimensional mappings; induced transformations},
language = {eng},
issn = {1099-4300},
journal = {Entropy},
title = {Entropy and Ergodicity of Boole-Type Transformations},
url = {https://doi.org/10.3390/e23111405},
volume = {23},
year = {2021}
}
TY - JOUR
ID - 2227819
AU - Blackmore, Denis - Balinsky, Alexander A - Kycia, Radoslaw Antoni - Prykarpatski, Anatolij K
PY - 2021
TI - Entropy and Ergodicity of Boole-Type Transformations
JF - Entropy
VL - 23
IS - 11
PB - MDPI AG, POSTFACH
SN - 10994300
KW - discrete transformations
KW - invariant measure
KW - ergodicity
KW - entropy
KW - Bernoulli type transformations
KW - Boole-type transformations
KW - fibered multidimensional mappings
KW - induced transformations
UR - https://doi.org/10.3390/e23111405
N2 - 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.
ER -
BLACKMORE, Denis, Alexander A BALINSKY, Radoslaw Antoni KYCIA a Anatolij K PRYKARPATSKI. Entropy and Ergodicity of Boole-Type Transformations. \textit{Entropy}. Basel (Schwitzerland): MDPI AG, POSTFACH, 2021, roč.~23, č.~11. ISSN~1099-4300. Dostupné z: https://dx.doi.org/10.3390/e23111405.
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