Entropy and Ergodicity of Boole-Type Transformations

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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BLACKMORE Denis BALINSKY Alexander A KYCIA Radoslaw Antoni PRYKARPATSKI Anatolij K

Rok publikování 2021
Druh Článek v odborném periodiku
Časopis / Zdroj Entropy
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.3390/e23111405
Doi http://dx.doi.org/10.3390/e23111405
Klíčová slova discrete transformations; invariant measure; ergodicity; entropy; Bernoulli type transformations; Boole-type transformations; fibered multidimensional mappings; induced transformations
Popis 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.
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