{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:10:07Z","timestamp":1766268607860,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,12]],"date-time":"2018-01-12T00:00:00Z","timestamp":1515715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013Hawking 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e20010056","type":"journal-article","created":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T04:01:55Z","timestamp":1515988915000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies"],"prefix":"10.3390","volume":"20","author":[{"given":"Christian","family":"Corda","sequence":"first","affiliation":[{"name":"Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha 82641, Iran"},{"name":"International Institute for Applicable Mathematics &amp; Information Sciences (IIAMIS), B.M. Birla Science Centre, Hyderabad 500 463, India"},{"name":"Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman 93630, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8965-9359","authenticated-orcid":false,"given":"Mehdi","family":"FatehiNia","sequence":"additional","affiliation":[{"name":"Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman 93630, Iran"},{"name":"Department of Mathematics, Yazd University, Yazd 89195-741, Iran"}]},{"given":"MohammadReza","family":"Molaei","sequence":"additional","affiliation":[{"name":"Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman 93630, Iran"}]},{"given":"Yamin","family":"Sayyari","sequence":"additional","affiliation":[{"name":"Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman 93630, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195007","DOI":"10.1088\/0264-9381\/32\/19\/195007","article-title":"Precise model of Hawking radiation from the tunnelling mechanism","volume":"32","author":"Corda","year":"2015","journal-title":"Class. 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