High frequency limits for invariant Ruelle densities
| Autor: | Colin Guillarmou, Tobias Weich, Joachim Hilgert |
|---|---|
| Přispěvatelé: | Université Paris-Saclay, Universität Paderborn (UPB), European Project: 725967,IPFLOW |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Dynamical Systems
Rank (linear algebra) Scalar (mathematics) FOS: Physical sciences Ocean Engineering Dynamical Systems (math.DS) 01 natural sciences Measure (mathematics) Mathematics - Spectral Theory Mathematics - Analysis of PDEs 0103 physical sciences Subsequence FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Invariant (mathematics) Mathematics - Dynamical Systems [MATH]Mathematics [math] Spectral Theory (math.SP) Mathematical Physics Mathematical physics Physics 010102 general mathematics State (functional analysis) Mathematical Physics (math-ph) Mathematics::Spectral Theory [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 010307 mathematical physics Laplace operator Analysis of PDEs (math.AP) [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] |
| Zdroj: | Annales Henri Lebesgue Annales Henri Lebesgue, UFR de Mathématiques-IRMAR, 2021, 4, pp.81-119. ⟨10.5802/ahl.67⟩ |
| ISSN: | 2644-9463 |
| DOI: | 10.5802/ahl.67⟩ |
| Popis: | 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. Comment: Minor changes, to appear at Annales Henri Lebesgue |
| Databáze: | OpenAIRE |
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