dark matter penetrates into the galactic center and its density profile becomes cuspy in the limit of $\lambda \rightarrow 0$. The role of the parameter $\alpha$ is to control the fraction of dark to luminous matter. Models with $\alpha \ll \alpha_{cr}$ are dominated by dark matter.

JH introduced a family of equilibrium DFs that reproduces $\Sigma_D(R)$ and depends on an integer constant $N$. This parameter controls the population of near-circular orbits and the disk temperature: the parameter $Q$ of @T64 decreases by increasing $N$. The DFs of JH have an isotropic part that determines the fraction of radial orbits. That isotropic part, which reconstructs the central density of the equilibrium state, shrinks to central regions of the galaxy as $N$ increases.

I apply my new method to the cored exponential disks of JH and calculate the spectrum of $\omega=\omega_R+{\rm i}\omega_I$. Subsequently, the eigenvector $\textbf{\textit{z}}_0$ is calculated from (\[eq:eigenvalue-problem-two\]) and it is used in (\[eq:a-versus-d\]) to compute $a^m_j(t)=e^{-{\rm i}\omega t}a^m_j(0)$ and the perturbed density $$\Sigma_1(R,\phi,t)= e^{\omega_I t} P_m(R) \cos \left [
m\phi \!-\! \omega_R t \!+\! \vartheta_m(R)\right ],
\label{eq:mode-shape}$$ which is the real part of (\[eq:expansion-sigma1-config\]). $P_m(R)$ and $\vartheta_m(R)$ are the amplitude and phase functions of an $m$-fold circumferential wave that 