Lower Resolvent Bounds and Lyapunov Exponents
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1508.04051.pdf
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675.54 KB
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dc3a2ec3caed127a3ba8b62ec7ae8837
Author(s)
Waters, Alden
Dyatlov, Semen
Date Issued
December 2015
Journal
Applied Mathematics Research eXpress
Publisher
Oxford University Press (OUP)
Citation
Dyatlov, Semyon and Alden Waters. “Lower Resolvent Bounds and Lyapunov Exponents.” Applied Mathematics Research eXpress 2016, 1 (December 2015): 68–97 © 2015 The Author(s)
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/AMRX/ABV010
