no. 2
Dynamical systems
Periodic points in the intersection of attracting immediate basins boundaries
[Points périodiques à l'intersection entre les frontières de bassins immédiats attractifs]

Présenté par : the Editorial Board

Rossetti, Bastien1
1 Laboratoire Émile-Picard, Université Paul-Sabatier, 31062 Toulouse, France
Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 222-225.

Nous donnons des conditions suffisantes pour que l'intersection entre les frontières de deux bassins immédiats attractifs d'une fraction rationnelle contienne au moins un point périodique.

We give conditions under which the intersection between two attracting immediate basins boundaries of a rational map contains at least one periodic point.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.09.004
Rossetti, Bastien 1

1 Laboratoire Émile-Picard, Université Paul-Sabatier, 31062 Toulouse, France 
@article{CRMATH_2017__355_2_222_0,
     author = {Rossetti, Bastien},
     title = {Periodic points in the intersection of attracting immediate basins boundaries},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {222--225},
     publisher = {Elsevier},
     volume = {355},
     number = {2},
     year = {2017},
     doi = {10.1016/j.crma.2016.09.004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2016.09.004/}
}
TY  - JOUR
AU  - Rossetti, Bastien
TI  - Periodic points in the intersection of attracting immediate basins boundaries
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 222
EP  - 225
VL  - 355
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2016.09.004/
DO  - 10.1016/j.crma.2016.09.004
LA  - en
ID  - CRMATH_2017__355_2_222_0
ER  - 
%0 Journal Article
%A Rossetti, Bastien
%T Periodic points in the intersection of attracting immediate basins boundaries
%J Comptes Rendus. Mathématique
%D 2017
%P 222-225
%V 355
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2016.09.004/
%R 10.1016/j.crma.2016.09.004
%G en
%F CRMATH_2017__355_2_222_0
Rossetti, Bastien. Periodic points in the intersection of attracting immediate basins boundaries. Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 222-225. doi : 10.1016/j.crma.2016.09.004. http://www.numdam.org/articles/10.1016/j.crma.2016.09.004/

[1] Carleson, L.; Gamelin, T.W. Complex Dynamics, Springer, 1995

[2] Mañé, R. On a theorem of Fatou, Bol. Soc. Bras. Mat., Volume 24 (1993), pp. 1-11

[3] Petersen, C.L. Local connectivity of some Julia sets containing a circle with an irrational rotation, Acta Math., Volume 177 (1996), pp. 163-224

[4] Pilgrim, K.M. Cylinders for iterated rational maps, University of California at Berkeley, CA, USA, 1994 (PhD thesis)

[5] Przytycki, F.; Urbański, M. Conformal Fractals: Ergodic Theory Methods, The London Mathematical Society Lecture Note Series, vol. 371, 2010

Cité par Sources :