2010/01/01 by Stéphane Nonnenmacher, Nonnenmacher, Stéphane
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #math-ph #math.AP #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.1004.4964
Notes of the minicourse given at the workshop "Spectrum and dynamics", Centre de Recherches Mathematiques, Montreal, April 2008.
arxiv created 2010/04/28 · openalex publication_date 2010/04/28 · arxiv updated 2010/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
These notes present a recent approach to study the high-frequency eigenstates of the Laplacian on compact Riemannian manifolds of negative sectional curvature. The main result is a lower bound on the Kolmogorov-Sinai entropy of the semiclassical measures associated with sequences of eigenstates, showing that high-frequency eigenstates cannot be too localized. The method is extended to the case of semiclassical Hamiltonian operators for which the classical flow in some energy range is of Anosov type, and to the case of quantized Anosov diffeomorphisms on the torus.