Consider a homogeneous space under a locally compact group G and a lattice Γ in G. Then the lattice naturally acts on the homogeneous space. Looking at a dense orbit, one may wonder how to describe its repartition. One then adopts a dynamical point of view and compare the asymptotic distribution of points in the orbits with the natural measure on the space. In the setting of Lie groups and their homogeneous spaces, several results show an equidistribution of points in the orbits.
We address here this problem in the setting of p-adic and S-arithmetic groups.
@article{CML_2010__2_1_1_0,
author = {Antonin Guilloux},
title = {Polynomial dynamic and lattice orbits in $S$-arithmetic homogeneous spaces},
journal = {Confluentes Mathematici},
pages = {1--35},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {1},
year = {2010},
doi = {10.1142/S1793744210000120},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744210000120/}
}
TY - JOUR AU - Antonin Guilloux TI - Polynomial dynamic and lattice orbits in $S$-arithmetic homogeneous spaces JO - Confluentes Mathematici PY - 2010 SP - 1 EP - 35 VL - 2 IS - 1 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744210000120/ DO - 10.1142/S1793744210000120 LA - en ID - CML_2010__2_1_1_0 ER -
%0 Journal Article %A Antonin Guilloux %T Polynomial dynamic and lattice orbits in $S$-arithmetic homogeneous spaces %J Confluentes Mathematici %D 2010 %P 1-35 %V 2 %N 1 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744210000120/ %R 10.1142/S1793744210000120 %G en %F CML_2010__2_1_1_0
Antonin Guilloux. Polynomial dynamic and lattice orbits in $S$-arithmetic homogeneous spaces. Confluentes Mathematici, Tome 2 (2010) no. 1, pp. 1-35. doi : 10.1142/S1793744210000120. https://cml.centre-mersenne.org/articles/10.1142/S1793744210000120/
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