Geodesic
Topological and metric properties of a one-dimensional dynamical system
Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1203-1242

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. 
@article{SM_2002_193_8_a4,
     author = {G. S. Chakvetadze},
     title = {Topological and metric properties of a one-dimensional dynamical system},
     journal = {Sbornik. Mathematics},
     pages = {1203--1242},
     publisher = {mathdoc},
     volume = {193},
     number = {8},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_8_a4/}
}
TY  - JOUR
AU  - G. S. Chakvetadze
TI  - Topological and metric properties of a one-dimensional dynamical system
JO  - Sbornik. Mathematics
PY  - 2002
SP  - 1203
EP  - 1242
VL  - 193
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2002_193_8_a4/
LA  - en
ID  - SM_2002_193_8_a4
ER  - 
%0 Journal Article
%A G. S. Chakvetadze
%T Topological and metric properties of a one-dimensional dynamical system
%J Sbornik. Mathematics
%D 2002
%P 1203-1242
%V 193
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2002_193_8_a4/
%G en
%F SM_2002_193_8_a4
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/