On the spectral theory and dynamics of asymptotically hyperbolic manifolds

2010/01/01 by Julie Rowlett · 3 citations
Mathematics · Physics and Astronomy · #Dynamics (music) #Geometric and Algebraic Topology #Geometry #Mathematical Dynamics and Fractals #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral analysis #math-ph #math.DG #math.DS #math.MP #math.SP #msc:37D40 #msc:53C22 #msc:58J50

paper · pdf · doi:10.5802/aif.2615

published in Annales de l’institut Fourier 60(7), 2461-2492 (Association of the Annals of the Fourier Institute) · This is a preliminary version of the article published in Annales de l'Institut Fourier. The final version is freely available online!

openalex publication_date 2010/01/01 · arxiv created 2020/12/11 · arxiv updated 2020/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.

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