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Study group "Patterson-Sullivan-Theorie": Guenda Palmirotta, "Patterson Sullivan distributions"

Abstract: Patterson-Sullivan distributions were introduced by Anantharman and Zelditch [AZ07] in the setting of
hyperbolic surfaces and generalizde to compact higher rank locally symmetric spaces by Hansen, Hilgert
and Schr ̈oder [HHS12]. In both cases they were introduced as Quantum Phase space distributions. More
recently it has been worked out (using a quantum classical correspondence) that on rank one locally
symmetric spaces Patterson-Sullivan distributions coincide with invariant Ruelle distributions [GHW21].
This correspondance led to high frequency limits of Ruelle distributions as well as to generalized Residue
formulas for Patterson-Sullivan distributions [SWB23].
Literature:
ˆAnantharaman and Zelditch, 2007 “Patterson-Sullivan distributions and quantum ergodicity”
ˆHansen, Hilgert, and Schröder, 2012 “Patterson-Sullivan distributions in higher rank”
ˆGuillarmou, Hilgert, and Weich, 2021 “High frequency limits for invariant Ruelle densities”
ˆSchütte, Weich and Barkhofen, 2023 “Meromorphic continuation of weighted zeta functions on
open hyperbolic systems”