  We investigate pole-skipping and its connection with quantum chaos,
emphasizing the role of the IR fixed point in the established relationship
between pole-skipping and a universal bound of the energy diffusion constant.
Using the holographic Gubser-Rocha model, which features a semi-locally
critical IR fixed point, we refine the pole-skipping argument to apply to
generic fixed points. Additionally, we explore the reconstruction of the full
hydrodynamic dispersion relation through pole-skipping. By considering
conditions in which the dispersion relation exhibits the energy diffusive mode
at low wave-vector and passes through a pole-skipping point, we propose an
effective heuristic approximation that relies on three physical quantities:
$(D_e, \, v_B, \, \lambda_L)$, determined from horizon data. Here, $D_e$
represents the energy diffusion constant, $v_B$ the butterfly velocity, and
$\lambda_L$ the Lyapunov exponent. Remarkably, this approximation demonstrates
excellent agreement with the quasi-normal mode, even extending its
applicability beyond the hydrodynamic regime.

High Energy Physics - Theory;Chaotic Dynamics