Invariant measures and arithmetic unique ergodicity
Annals of mathematics, Tome 163 (2006) no. 1, pp. 165-219
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We classify measures on the locally homogeneous space $\Gamma \backslash SL(2,\mathbb{R}) \times L$ which are invariant and have positive entropy under the diagonal subgroup of $SL(2,\mathbb{R})$ and recurrent under $L$. This classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the finite volume case. Other applications are also presented.
@article{10_4007_annals_2006_163_165,
author = {Elon Lindenstrauss},
title = {Invariant measures and arithmetic unique ergodicity},
journal = {Annals of mathematics},
pages = {165--219},
publisher = {mathdoc},
volume = {163},
number = {1},
year = {2006},
doi = {10.4007/annals.2006.163.165},
mrnumber = {2195133},
zbl = {1104.22015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.165/}
}
TY - JOUR AU - Elon Lindenstrauss TI - Invariant measures and arithmetic unique ergodicity JO - Annals of mathematics PY - 2006 SP - 165 EP - 219 VL - 163 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.165/ DO - 10.4007/annals.2006.163.165 LA - en ID - 10_4007_annals_2006_163_165 ER -
Elon Lindenstrauss. Invariant measures and arithmetic unique ergodicity. Annals of mathematics, Tome 163 (2006) no. 1, pp. 165-219. doi: 10.4007/annals.2006.163.165
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