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 $γ$ 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 $γ$, and gives the minimal number of derivatives lost in exponential decay of solutions to the wave equation.

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