Quantum Monodromy and nonconcentration near a closed semi-hyperbolic orbit

DOI10.1090/S0002-9947-2011-05321-3zbMath1230.58020arXiv0803.0697OpenAlexW2041539660MaRDI QIDQ5200191

Hans Christianson

Publication date: 1 August 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0697

zbMATH Keywords

boundary value problemseigenfunctionsDistributions

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Resonance in context of PDEs (35B34) Noncommutative global analysis, noncommutative residues (58J42) PDEs on manifolds (35R01)

Related Items (20)

Semiclassical Quantum Maps of Semi-Hyperbolic Type ⋮ Strong scarring of logarithmic quasimodes ⋮ Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions ⋮ Near sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping ⋮ Semiclassical diffraction by conormal potential singularities ⋮ Construction of nonlinear quasimodes near elliptic periodic orbits ⋮ Resolvent estimates for normally hyperbolic trapped sets ⋮ Cutoff resolvent estimates and the semilinear Schrödinger equation ⋮ Quantum ergodicity for a class of mixed systems ⋮ High-frequency resolvent estimates on asymptotically Euclidean warped products ⋮ Eigenmodes of the damped wave equation and small hyperbolic subsets ⋮ Semiclassical resonances associated with a periodic orbit ⋮ Local smoothing for the Schrödinger equation on a multi-warped product manifold with inflection-transmission trapping ⋮ Imperfect geometric control and overdamping for the damped wave equation ⋮ On resonances generated by conic diffraction ⋮ Unique continuation for quasimodes on surfaces of revolution: rotationally invariant neighbourhoods ⋮ High-Frequency Dynamics for the Schrödinger Equation, with Applications to Dispersion and Observability ⋮ From resolvent estimates to damped waves ⋮ A Non-Concentration Estimate for Partially Rectangular Billiards ⋮ Decay of correlations for normally hyperbolic trapping

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