On the dynamics of dominated splitting
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
Affiliations des auteurs :
Enrique R. Pujals 1 ; Martín Sambarino 2
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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 -
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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
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