Mathematical Research Letters
Volume 22 (2015)
Non-trapping surfaces of revolution with long-living resonances
Pages: 23 – 42
We study resonances of surfaces of revolution obtained by removing a disk from a cone and attaching a hyperbolic cusp in its place. These surfaces include ones with non-trapping geodesic flow (every maximally extended non-reflected geodesic is unbounded) and yet infinitely many long-living resonances (resonances with uniformly bounded imaginary part, i.e., decay rate).