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Rényi Entropies of Dynamical Systems: A Generalization Approach | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 1 - شماره پیاپی 24، فروردین 2023، صفحه 15-33 اصل مقاله (518.76 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2022.18206.1168 | ||
| نویسندگان | ||
| Zahra Eslami Giski* 1؛ Hossein Fathizadeh2؛ Somayeh Ghiasi Hafezi1 | ||
| 1Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran | ||
| 2Department of Economics, Sirjan Branch, Islamic Azad University, Sirjan, Iran | ||
| چکیده | ||
| Entropy measures have received considerable attention in quantifying the structural complexity of real-world systems and are also used as measures of information obtained from a realization of the considered experiments. In the present study, new notions of entropy for a dynamical system are introduced. The Rényi entropy of measurable partitions of order and its conditional version are defined, and some important properties of these concepts are studied. It is shown that the Shannon entropy and its conditional version for measurable partitions can be obtained as the limit of their Rényi entropy and conditional Rényi entropy. In addition, using the suggested concept of Rényi entropy for measurable partitions, the Rényi entropy for dynamical systems is introduced. It is also proved that the Rényi entropy for dynamical systems is invariant under isomorphism. | ||
| کلیدواژهها | ||
| Measurable partition؛ Rényi entropy؛ Conditional Rényi entropy؛ Dynamical system | ||
| مراجع | ||
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