Abstract:
The iterates of the real rational function $s_{a,b}(x)=b-ax/(1+x^2)$ are studied in their dependence on the parameters $a,b\in\mathbb R$. The parameter ranges corresponding to regular and chaotic dynamical behaviour of the system are determined. In particular, an analogue of Jakobson's theorem is proved for a two-parameter family of one-dimensional maps close to a certain map with a neutral fixed point.
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