Stable ergodicity of certain linear automorphisms of the torus
Annals of mathematics, Tome 162 (2005) no. 1, pp. 65-107
We find a class of ergodic linear automorphisms of $\mathbb{T}^N$ that are stably ergodic. This class includes all non-Anosov ergodic automorphisms when $N=4$. As a corollary, we obtain the fact that all ergodic linear automorphism of $\mathbb{T}^N$ are stably ergodic when $N\leq 5$.
@article{10_4007_annals_2005_162_65,
author = {Federico Rodriguez Hertz},
title = {Stable ergodicity of certain linear automorphisms of the torus},
journal = {Annals of mathematics},
pages = {65--107},
year = {2005},
volume = {162},
number = {1},
doi = {10.4007/annals.2005.162.65},
mrnumber = {2201693},
zbl = {1098.37028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.65/}
}
TY - JOUR AU - Federico Rodriguez Hertz TI - Stable ergodicity of certain linear automorphisms of the torus JO - Annals of mathematics PY - 2005 SP - 65 EP - 107 VL - 162 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.65/ DO - 10.4007/annals.2005.162.65 LA - en ID - 10_4007_annals_2005_162_65 ER -
%0 Journal Article %A Federico Rodriguez Hertz %T Stable ergodicity of certain linear automorphisms of the torus %J Annals of mathematics %D 2005 %P 65-107 %V 162 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.65/ %R 10.4007/annals.2005.162.65 %G en %F 10_4007_annals_2005_162_65
Federico Rodriguez Hertz. Stable ergodicity of certain linear automorphisms of the torus. Annals of mathematics, Tome 162 (2005) no. 1, pp. 65-107. doi: 10.4007/annals.2005.162.65
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