Dynamics of potts–bethe mapping of degree four on ℚ5
We give the full descriptions of the dynamical behaviour of the Potts–Bethe mapping of degree four on Q5. For a, b in Q5, the Potts–Bethe mapping is written as follows f_{a,b}=( \frac{ax+b}{x+a+b-1})^4 When |a - 1|5 < |b + 1|5 < 1, there exists a subsystem (J; f_{a,b}) that is topologically...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English English |
| Published: |
American Institute of Physics Inc.
2019
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/78488/ http://irep.iium.edu.my/78488/18/78488_Dynamics%20of%20potts%E2%80%93bethe%20mapping%20of%20degree_complete_latest.pdf http://irep.iium.edu.my/78488/7/78488_Dynamics%20of%20potts%E2%80%93bethe%20mapping%20of%20degree_scopus.pdf |
| _version_ | 1848788616439922688 |
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| author | Ahmad, Mohd Ali Khameini Pah, Chin Hee Saburov, Mansoor |
| author_facet | Ahmad, Mohd Ali Khameini Pah, Chin Hee Saburov, Mansoor |
| author_sort | Ahmad, Mohd Ali Khameini |
| building | IIUM Repository |
| collection | Online Access |
| description | We give the full descriptions of the dynamical behaviour of the Potts–Bethe mapping of degree four on Q5. For a, b in Q5, the Potts–Bethe mapping is written as follows
f_{a,b}=( \frac{ax+b}{x+a+b-1})^4
When |a - 1|5 < |b + 1|5 < 1, there exists a subsystem (J; f_{a,b}) that is topologically conjugate to the chaotic full shift dynamics on four symbols.We also show that for any initial point x in Q5, the trajectory of the Potts–Bethe mapping
converges to a unique attracting fixed point. |
| first_indexed | 2025-11-14T17:43:39Z |
| format | Proceeding Paper |
| id | iium-78488 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T17:43:39Z |
| publishDate | 2019 |
| publisher | American Institute of Physics Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-784882020-07-15T03:46:11Z http://irep.iium.edu.my/78488/ Dynamics of potts–bethe mapping of degree four on ℚ5 Ahmad, Mohd Ali Khameini Pah, Chin Hee Saburov, Mansoor QA Mathematics We give the full descriptions of the dynamical behaviour of the Potts–Bethe mapping of degree four on Q5. For a, b in Q5, the Potts–Bethe mapping is written as follows f_{a,b}=( \frac{ax+b}{x+a+b-1})^4 When |a - 1|5 < |b + 1|5 < 1, there exists a subsystem (J; f_{a,b}) that is topologically conjugate to the chaotic full shift dynamics on four symbols.We also show that for any initial point x in Q5, the trajectory of the Potts–Bethe mapping converges to a unique attracting fixed point. American Institute of Physics Inc. 2019-12-04 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/78488/18/78488_Dynamics%20of%20potts%E2%80%93bethe%20mapping%20of%20degree_complete_latest.pdf application/pdf en http://irep.iium.edu.my/78488/7/78488_Dynamics%20of%20potts%E2%80%93bethe%20mapping%20of%20degree_scopus.pdf Ahmad, Mohd Ali Khameini and Pah, Chin Hee and Saburov, Mansoor (2019) Dynamics of potts–bethe mapping of degree four on ℚ5. In: "1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018", 10 - 12 Dec 2018, Penang. https://aip.scitation.org/doi/pdf/10.1063/1.5136355 10.1063/1.5136355 |
| spellingShingle | QA Mathematics Ahmad, Mohd Ali Khameini Pah, Chin Hee Saburov, Mansoor Dynamics of potts–bethe mapping of degree four on ℚ5 |
| title | Dynamics of potts–bethe mapping of degree four on ℚ5 |
| title_full | Dynamics of potts–bethe mapping of degree four on ℚ5 |
| title_fullStr | Dynamics of potts–bethe mapping of degree four on ℚ5 |
| title_full_unstemmed | Dynamics of potts–bethe mapping of degree four on ℚ5 |
| title_short | Dynamics of potts–bethe mapping of degree four on ℚ5 |
| title_sort | dynamics of potts–bethe mapping of degree four on ℚ5 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/78488/ http://irep.iium.edu.my/78488/ http://irep.iium.edu.my/78488/ http://irep.iium.edu.my/78488/18/78488_Dynamics%20of%20potts%E2%80%93bethe%20mapping%20of%20degree_complete_latest.pdf http://irep.iium.edu.my/78488/7/78488_Dynamics%20of%20potts%E2%80%93bethe%20mapping%20of%20degree_scopus.pdf |