Lower resolvent bounds and Lyapunov exponents

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.

26 pages, 3 figures; to appear in Appl. Math. Research Express

References in corpus (3)

• Spectral gaps, additive energy, and a fractal uncertainty principle
• Spectral gaps for normally hyperbolic trapping
• Concentration Of Laplace Eigenfunctions And Stabilization Of Weakly Damped Wave Equation

Cited by in corpus (2)

• Improved fractal Weyl bounds for hyperbolic manifolds
• Exponential lower resolvent bounds far away from trapped sets