Francois Ledrappier (Ecole Polytechnique)

Distribution results for cocompact groups in $SL(2,\mathbb{Q} _p)$

Abstract. This report on a joint work with Mark Pollicott. We continue our study of linear actions of lattices $\Gamma$ (and of their coabelian subgroups $\overline \Gamma$) in SL₂ by investigating the case of the field of p-adic numbers. Results are similar to the ones in the cases of $\mathbb{R}$ or $\mathbb{C}$, with the following new features:

- an equidistribution result for the eigenvalues of matrices in $\Gamma$or $\overline \Gamma$.

- a complete description of the $\overline \Gamma$ invariant measures on the space ${\mathbb{Q} }_p \times {\mathbb{Q} }_p$.