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Mathematics > Analysis of PDEs

Title: High frequency limits for invariant Ruelle densities

Abstract: 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 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.
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Dynamical Systems (math.DS); Spectral Theory (math.SP)
Cite as: arXiv:1803.06717 [math.AP]
  (or arXiv:1803.06717v1 [math.AP] for this version)

Submission history

From: Tobias Weich [view email]
[v1] Sun, 18 Mar 2018 19:05:41 GMT (48kb,D)