Corda Christian, FatehiNia Mehdi, Molaei MohammadReza, Sayyari Yamin
Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha 82641, Iran.
International Institute for Applicable Mathematics & Information Sciences (IIAMIS), B.M. Birla Science Centre, Hyderabad 500 463, India.
Entropy (Basel). 2018 Jan 12;20(1):56. doi: 10.3390/e20010056.
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 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 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 and the average entropy is investigated.
在本文中，我们考虑从黑洞推导出来的迭代函数系统映射的度量熵，这些熵即贝肯斯坦 - 霍金熵及其次主导修正。更确切地说，我们考虑最近文献中一些论文所分析的类玻尔黑洞的模型，得到了一个有趣的结果：黑洞的度量熵由函数的度量熵产生，而函数的度量熵由黑洞主量子数产生，即由黑洞量子能级产生。我们基于一种新型的覆盖逆为一般迭代函数系统提出了一种新型拓扑熵。然后考虑了迭代函数系统（IFS）的度量熵概念，并证明了这些拓扑熵的定义是等价的。结果表明，这种拓扑熵保持了连续映射拓扑熵经典定义所具有的一些性质。我们还将基于其元素的拓扑熵的另一种类型的拓扑熵视为IFS的拓扑熵，并且它在拓扑共轭下也是一个不变对象。研究了公理与平均熵之间的关系。
