Dynamics of potts–bethe mapping of degree four on ℚ5

• Main Authors: Ahmad, Mohd Ali Khameini, Pah, Chin Hee, Saburov, Mansoor
• Format: Conference or Workshop Item
• Language: English; English
• Published: American Institute of Physics Inc. 2019
• Subjects: QA Mathematics
• Online Access: 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; http://irep.iium.edu.my/78488/; https://aip.scitation.org/doi/pdf/10.1063/1.5136355
• Institution: Universiti Islam Antarabangsa Malaysia

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.