Dynamics of potts–bethe mapping of degree four on ℚ5 - Ahmad, Mohd Ali Khameini; Pah, Chin Hee; Saburov, Mansoor (American Institute of Physics Inc., 2019)
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.