High frequency limits for invariant Ruelle densities

We establish an equidistribution result for Ruelle resonant states on compact locally symmetric spaces of rank 1. More precisely, we prove that among the first band resonances there is a density one subsequence such respective products and co-resonant converge weakly to Liouville measure. this by establishing explicit quantum-classical correspondence between eigenspaces scalar Laplacian resonances, which also leads new description Patterson–Sullivan distributions.