Colin Guillarmou

Pollicott–Ruelle Resonances for Open Systems

We define Pollicott–Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of the meromorphic continuation of the resolvent of the generator of the flow and they describe decay of classical correlations. As an application, we show that the Ruelle zeta function extends meromorphically to the entire complex plane.

Resolvent at low energy III: The spectral measure

The second and third authors were supported by Australian Research Council Discovery grants DP0771826 and DP1095448 and the second author by a Future Fellowship. The first author was partially supported by ANR grant ANR-09-JCJC-0099-01 and by the PICS-CNRS Progress in Geometric Analysis and Applications, and thanks the math department of ANU for its hospitality.

Generalized Krein formula, determinants, and Selberg zeta function in even dimension

For a class of even dimensional asymptotically hyperbolic (AH) manifolds, we develop a generalized Birman-Krein theory to study scattering asymptotics and, when the curvature is constant, to analyze the Selberg zeta function. The main objects we construct for an AH manifold

Identification of a Connection from Cauchy Data on a Riemann Surface with Boundary

(X,g)

Power spectrum of the geodesic flow on hyperbolic manifolds

are, on the one hand, a natural spectral function

Classical and quantum resonances for hyperbolic surfaces

\xi

Scattering Phase Asymptotics with Fractal Remainders

for the Laplacian

Marked boundary rigidity for surfaces

\Delta_g

Random Walk on Surfaces with Hyperbolic Cusps

, which replaces the counting function of the eigenvalues in this infinite volume case, and on the other hand the determinant of the scattering operator

Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds

S_X(\lambda)