Lower Resolvent Bounds and Lyapunov Exponents
We prove a new polynomial lower bound on the scattering resolvent. For that, we construct a quasimode localized on a trajectory \gamma which is trapped in the past, but not in the future. The power in the bound is expressed in terms of the maximal Lyapunov exponent on \gamma , and gives the minimal...
| Main Authors: | , |
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| Format: | Article |
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Oxford University Press (OUP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/115825 https://orcid.org/0000-0002-6594-7604 |
| Summary: | We prove a new polynomial lower bound on the scattering resolvent. For that, we construct a quasimode localized on a trajectory \gamma which is trapped in the past, but not in the future. The power in the bound is expressed in terms of the maximal Lyapunov exponent on \gamma , and gives the minimal number of derivatives lost in exponential decay of solutions to the wave equation. |
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