High frequency limits for invariant Ruelle densities
Annales Henri Lebesgue, Volume 4 (2021), pp. 81-119.


Keywords Ruelle resonances, quantum ergodicity, semi-classical measures


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 Ruelle resonances there is a density one subsequence such that the respective products of resonant and co-resonant states converge weakly to the Liouville measure. We prove this result by establishing an explicit quantum-classical correspondence between eigenspaces of the scalar Laplacian and the resonant states of the first band of Ruelle resonances, which also leads to a new description of Patterson–Sullivan distributions.


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