English

High frequency limits for invariant Ruelle densities

Analysis of PDEs 2020-10-02 v2 Mathematical Physics Dynamical Systems math.MP Spectral Theory

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.

Keywords

Cite

@article{arxiv.1803.06717,
  title  = {High frequency limits for invariant Ruelle densities},
  author = {Colin Guillarmou and Joachim Hilgert and Tobias Weich},
  journal= {arXiv preprint arXiv:1803.06717},
  year   = {2020}
}

Comments

Minor changes, to appear at Annales Henri Lebesgue

R2 v1 2026-06-23T00:56:54.473Z