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: | Conference or Workshop Item |
| 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/ 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 |
| Summary: | 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. |
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