Laplacian spectrum and decay of geodesic flow correlations on hyperbolic surfaces (I)

Abstract

Using PSL(2, R) representation theory, we study the temporal correlations of two observables propagated by the geodesic flow of a hyperbolic surface. If the observables are sufficiently regular, these correlations can be developed asymptotically in an exponentially decreasing manner. Ruelle resonances and their link to eigenfunctions of the Laplacian appear explicitly.

Laplacian spectrum and decay of geodesic flow correlations on hyperbolic surfaces (I)

Abstract

Events

Graph and surface spectra (1)

Curves, Surfaces and Intersection

Regular graphs : Laplacian spectrum and geodesic flow correlation decay (1)

Prescribing the Spectra of Cubic Graphs

Regular graphs : Laplacian spectrum and decay of geodesic flow correlations (2)

Circuit QED Lattices: From Synthetic Quantum Systems to Spectral Graph The…

Laplacian spectrum and decay of geodesic flow correlations on hyperbolic surfaces (I)

Determinants of Laplacians and Random Surfaces

Laplacian spectrum and decay of geodesic flow correlations on hyperbolic surfaces (II)

Spectral projectors on hyperbolic surfaces

Regularity of resonant states on a compact hyperbolic surface

Poincaré Series and Convex Bodies on Flat Tori

Value in 0 of the Poincaré series of surfaces and graphs

Ruelle resonances for the geodesic flow on non-compact varieties

Optimal spectral hole for random regular graphs, after J. Friedman (I)

Low-Temperature Quantum Bounds on Curved Manifolds

Optimal spectral hole for random regular graphs, after J. Friedman (II)

From the geodesic flow to the wave equation on an Anosov variety

See also