### Two New Types of Chaotic Maps and Minimal Systems

Received: 5 September 2014     Accepted: 16 September 2014     Published: 17 September 2014
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.

Keywords

Topologically θ - Transitive Map, α- Chaotic, Chaotic Amp, α- Transitive, θ- Dense

References
• 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

AMA 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  - ```
Author Information
• University of Sulaimani, Faculty of Science and Science Education, School of Science, Math Department

• University of Sulaimani, Faculty of physical and Basie Education, School of Basic Education, Department of Computer Science

• Sections