In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). The two notions are defined by using the concepts of α-transitive map and θ-transitive map respectively Also, we define and study the relationship between two types of minimal mappings, namely, α - minimal mapping and θ-minimal mapping, The main results are the following propositions: 1). Every topologically α-chaotic map is a chaotic map which implies topologically θ- chaotic map, but the converse not necessarily true. 2). Every α-minimal map is a minimal map which implies θ- minimal map in topological spaces, but the converse not necessarily true.
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Pure and Applied Mathematics Journal (Volume 3, Issue 6-1)
This article belongs to the Special Issue Mathematical Theory and Modeling |
DOI | 10.11648/j.pamj.s.2014030601.12 |
Page(s) | 7-12 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2014. Published by Science Publishing Group |
Topologically θ - Transitive Map, α- Chaotic, Chaotic Amp, α- Transitive, θ- Dense
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APA Style
Mohammed Nokhas Murad Kaki, Sherko Hassan Abdurrahman. (2014). Two New Types of Chaotic Maps and Minimal Systems. Pure and Applied Mathematics Journal, 3(6-1), 7-12. https://doi.org/10.11648/j.pamj.s.2014030601.12
ACS Style
Mohammed Nokhas Murad Kaki; Sherko Hassan Abdurrahman. Two New Types of Chaotic Maps and Minimal Systems. Pure Appl. Math. J. 2014, 3(6-1), 7-12. doi: 10.11648/j.pamj.s.2014030601.12
@article{10.11648/j.pamj.s.2014030601.12, author = {Mohammed Nokhas Murad Kaki and Sherko Hassan Abdurrahman}, title = {Two New Types of Chaotic Maps and Minimal Systems}, journal = {Pure and Applied Mathematics Journal}, volume = {3}, number = {6-1}, pages = {7-12}, doi = {10.11648/j.pamj.s.2014030601.12}, url = {https://doi.org/10.11648/j.pamj.s.2014030601.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030601.12}, abstract = {In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). The two notions are defined by using the concepts of α-transitive map and θ-transitive map respectively Also, we define and study the relationship between two types of minimal mappings, namely, α - minimal mapping and θ-minimal mapping, The main results are the following propositions: 1). Every topologically α-chaotic map is a chaotic map which implies topologically θ- chaotic map, but the converse not necessarily true. 2). Every α-minimal map is a minimal map which implies θ- minimal map in topological spaces, but the converse not necessarily true.}, year = {2014} }
TY - JOUR T1 - Two New Types of Chaotic Maps and Minimal Systems AU - Mohammed Nokhas Murad Kaki AU - Sherko Hassan Abdurrahman Y1 - 2014/09/17 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.s.2014030601.12 DO - 10.11648/j.pamj.s.2014030601.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 7 EP - 12 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2014030601.12 AB - In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). The two notions are defined by using the concepts of α-transitive map and θ-transitive map respectively Also, we define and study the relationship between two types of minimal mappings, namely, α - minimal mapping and θ-minimal mapping, The main results are the following propositions: 1). Every topologically α-chaotic map is a chaotic map which implies topologically θ- chaotic map, but the converse not necessarily true. 2). Every α-minimal map is a minimal map which implies θ- minimal map in topological spaces, but the converse not necessarily true. VL - 3 IS - 6-1 ER -