Metadata
Abstract
We establish an equidistribution result for Ruelle resonant states on compact locally symmetric spaces of rank . 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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