$p$-adic dynamical systems of the function $\frac{ax}{x^2+a}$

U. A. Rozikov, I. A. Sattarov, S. Yam

We show that any $(1,2)$-rational function with a unique fixed point is topologically conjugate to a $(2,2)$-rational function or to the function $f(x)=\frac{ax}{x^2+a}$. The case $…