Lower Resolvent Bounds and Lyapunov Exponents
Author(s)
Waters, Alden; Dyatlov, Semen
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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.
Date issued
2015-12Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1687-1200
1687-1197