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Entropy 2018, 20(1), 56; https://doi.org/10.3390/e20010056

Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

1
Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha 82641, Iran
2
International Institute for Applicable Mathematics & Information Sciences (IIAMIS), B.M. Birla Science Centre, Hyderabad 500 463, India
3
Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman 93630, Iran
4
Department of Mathematics, Yazd University, Yazd 89195-741, Iran
*
Author to whom correspondence should be addressed.
Received: 16 November 2017 / Revised: 5 January 2018 / Accepted: 10 January 2018 / Published: 12 January 2018
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Abstract

In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S ) is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated. View Full-Text
Keywords: iterated function system; Axiom A; metric entropy; topological entropy; black hole entropy; Bohr-like black hole iterated function system; Axiom A; metric entropy; topological entropy; black hole entropy; Bohr-like black hole
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Corda, C.; FatehiNia, M.; Molaei, M.; Sayyari, Y. Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies. Entropy 2018, 20, 56.

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