Geodesic
Topological and metric properties of a one-dimensional dynamical system
Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1203-1242 
G. S. Chakvetadze. Topological and metric properties of a one-dimensional dynamical system. Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1203-1242. http://geodesic.mathdoc.fr/item/SM_2002_193_8_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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