Mathematical Research Letters

Volume 22 (2015)

Number 1

Non-trapping surfaces of revolution with long-living resonances

Pages: 23 – 42

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n1.a3

Authors

Kiril R. Datchev (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.; and Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Daniel D. Kang (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Andre P. Kessler (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

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).

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