  Local density of states (LDOS) is emerging as powerful means of exploring
synthetic topological phases. However, the current LDOS detection method
remains rare and merely works for static situations. Here, we introduce a
generic dynamical method to detect both the static and Floquet LDOS, based on
an elegant connection between dynamics of chiral density and local spectral
densities. Moreover, we find that the Floquet LDOS allows to measure out
Floquet quasienergy spectra and identify topological $\pi$ modes. As an
example, we demonstrate that both the static and Floquet higher-order
topological phase can be universally identified via LDOS detection, regardless
of whether the topological corner modes are in energy gaps, bands or continue
energy spectra without bandgaps. Our study opens a new avenue utilizing
dynamics to detect topological spectral densities and provides a universal
approach of identifying static and Floquet topological phases.
