R-norm entropy for partitions of algebraic structures and dynamical systems

	R-norm entropy for partitions of algebraic structures and dynamical systems
International Journal of Nonlinear Analysis and Applications
مقاله 29، دوره 15، شماره 3، خرداد 2024، صفحه 357-369 اصل مقاله (408.27 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24569.2772
نویسندگان
Haji Mohammad Hosein Zarenezhad؛ Javad Jamalzadeh^*
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran
چکیده
In this paper, we define R-norm entropy and conditional R-norm entropy of partitions of algebraic structures, and we establish some of their basic properties. We show that the Shannon entropy and the conditional Shannon entropy of partitions can be derived from the R-norm entropy and the conditional R-norm entropy of partitions, respectively, by letting R tend to 1. Finally, using the notion of entropy for partitions, we define the R-norm entropy of a dynamical system. We prove that the R-norm entropies of isomorphic dynamical systems are equal.
کلیدواژه‌ها
Algebraic structure؛ R-norm entropy؛ partition؛ conditional R-norm entropy؛ dynamical system؛ isomorphism
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