Geodesic
On the dynamics of dominated splitting
Enrique R. Pujals1 ; Martín Sambarino2
1 Instituto de Matemática Pura e Aplicada<br/>22460-320 Rio de Janeiro, R.J.<br/>Brazil
2 Facultad de Ciencias - Centro de Matemática<br/>Universidad de la República<br/>11400 Montevideo<br/>Uruguay
Annals of mathematics, Tome 169 (2009) no. 3, pp. 675-740.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $f:M\to M$ be a $C^2$ diffeomorphism of a compact surface. We give a complete description of the dynamics of any compact invariant set having dominated splitting. In particular, we prove a Spectral Decomposition Theorem for the limit set $L(f)$ under the assumption of dominated splitting. Moreover, we describe all the bifurcations that these systems can exhibit and the different types of dynamics that could follow for small $C^r-$perturbations.
DOI : 10.4007/annals.2009.169.675

Enrique R. Pujals 1 ; Martín Sambarino 2

1 Instituto de Matemática Pura e Aplicada<br/>22460-320 Rio de Janeiro, R.J.<br/>Brazil
2 Facultad de Ciencias - Centro de Matemática<br/>Universidad de la República<br/>11400 Montevideo<br/>Uruguay 
@article{10_4007_annals_2009_169_675,
     author = {Enrique R. Pujals and Mart{\'\i}n Sambarino},
     title = {On the dynamics of dominated splitting},
     journal = {Annals of mathematics},
     pages = {675--740},
     publisher = {mathdoc},
     volume = {169},
     number = {3},
     year = {2009},
     doi = {10.4007/annals.2009.169.675},
     mrnumber = {2480616

},
     zbl = {1178.37032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.675/}
}
TY  - JOUR
AU  - Enrique R. Pujals
AU  - Martín Sambarino
TI  - On the dynamics of dominated splitting
JO  - Annals of mathematics
PY  - 2009
SP  - 675
EP  - 740
VL  - 169
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.675/
DO  - 10.4007/annals.2009.169.675
LA  - en
ID  - 10_4007_annals_2009_169_675
ER  - 
%0 Journal Article
%A Enrique R. Pujals
%A Martín Sambarino
%T On the dynamics of dominated splitting
%J Annals of mathematics
%D 2009
%P 675-740
%V 169
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.675/
%R 10.4007/annals.2009.169.675
%G en
%F 10_4007_annals_2009_169_675
Enrique R. Pujals; Martín Sambarino. On the dynamics of dominated splitting. Annals of mathematics, Tome 169 (2009) no. 3, pp. 675-740. doi : 10.4007/annals.2009.169.675. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.675/

Cité par Sources :