4 problems

Let $P$ be the generator associated with an open hyperbolic system, and suppose that the trapped set in $p^{-1}(1)$ is $E_0^*\cap p^{-1}(1)$ and has dimension $\delta$. For any…

Let $N(r,\gamma)$ denote the resonance counting function in a strip of depth $\gamma$, let $d_H$ be the fractal dimension parameter associated with the trapped set, and let…

Let the resonance density be the density of quantum resonances in the high-frequency limit, and let the fractal Weyl law provide an upper bound on its exponential growth. Sharpness…

Let $X=\Gamma\backslash\mathbb{H}^{n+1}$ be a convex co-compact hyperbolic manifold, and let the resonances in the relevant strip be counted as in the preceding resonance-counting…