Entropy of semiclassical measures in dimension 2

DOI10.1215/00127094-2010-056zbMath1230.37048arXiv0809.0230OpenAlexW2064707438MaRDI QIDQ616586

Gabriel Rivière

Publication date: 10 January 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.0230

zbMATH Keywords

geodesic flowLaplacianKolmogorov-Sinai entropysemiclassical measurecompact Riemannian surface

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (13)

Cylindrical Wigner measures ⋮ A Haar component for quantum limits on locally symmetric spaces ⋮ Semiclassical measures for higher-dimensional quantum cat maps ⋮ Entropy of semiclassical measures for nonpositively curved surfaces ⋮ Singularity of projections of 2-dimensional measures invariant under the geodesic flow ⋮ Macroscopic limits of chaotic eigenfunctions ⋮ Joint quasimodes, positive entropy, and quantum unique ergodicity ⋮ Superscars for arithmetic toral point scatterers ⋮ Delocalization of slowly damped eigenmodes on Anosov manifolds ⋮ Projections of Measures Invariant Under the Geodesic Flow ⋮ High-Frequency Dynamics for the Schrödinger Equation, with Applications to Dispersion and Observability ⋮ Control of eigenfunctions on surfaces of variable curvature ⋮ Around quantum ergodicity

Cites Work

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• Entropic bounds on semiclassical measures for quantized one-dimensional maps
• Entropy of semiclassical measures for nonpositively curved surfaces
• Entropy of semiclassical measures of the Walsh-quantized Baker's map
• Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)
• Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus
• Ergodicity and eigenfunctions of the Laplacian
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• Scarred eigenstates for quantum cat maps of minimal periods
• On the maximal scarring for quantum cat map eigenstates
• Hecke theory and equidistribution for the quantization of linear maps of the torus
• Asymptotic distribution of resonances for convex obstacles
• Uniform semiclassical estimates for the propagation of quantum observables.
• Equipartition of the eigenfunctions of quantized ergodic maps on the torus
• Entropy and the localization of eigenfunctions
• Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
• Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
• An inequality for the entropy of differentiable maps
• Introduction to Dynamical Systems

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