High frequency limits for invariant Ruelle densities

摘要: We establish an equidistribution result for Ruelle resonant states on compact locally symmetric spaces of rank one. 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 which also leads new description Patterson-Sullivan distributions.