  The numerical study indicates that there exists a relation between the
quasinormal modes and the Davies point for a black hole. In this paper, we
analytically study this relation for the charged Reissner-Nordstr\"{o}m black
holes in asymptotically flat and dS spacetimes. In the eikonal limit, the
angular velocity $\Omega$ and the Lyapunov exponent $\lambda$ of the photon
sphere, respectively, corresponding to the real and imaginary parts of the
quasinormal modes are obtained from the null geodesics. Both in asymptotically
flat and dS spacetimes, we observe the spiral-like shapes in the complex
quasinormal mode plane. However, the starting point of the shapes do not
coincide with the Davies point. Nevertheless, we find a new relation that the
Davies point exactly meet the maximum of the temperature $T$ in the
$T$-$\Omega$ and $T$-$\lambda$ planes. In higher dimensional asymptotically
flat spacetime, even there is no the spiral-like shape, such relation still
holds. Therefore, we provide a new relation between the black hole
thermodynamics and dynamics. Applying this relation, we can test the black hole
thermodynamic property by the quasinormal modes.

General Relativity and Quantum Cosmology;High Energy Physics - Theory