Local Petrovskii lacunas close to parabolic singular points of the wavefronts of strictly hyperbolic partial differential equations

We enumerate the local Petrovskii lacunas (that is, the domains of local regularity of the principal fundamental solutions of strictly hyperbolic PDEs with constant coefficients in $\mathbb{R}^N$) close to parabolic singular points of their wavefronts (that is, at the points of types $P_8^1$, $P_8^2$, $\pm X_9$, $X_9^1$, $X_9^2$, $J_{10}^1$ and $J_{10}^3$). These points form the next most difficult family of classes in the natural classification of singular points after the so-called simple singularities $A_k$, $D_k$, $E_6$, $E_7$ and $E_8$, which have been investigated previously.
Also we present a computer program which counts the topologically distinct morsifications of critical points of smooth functions, and hence also the local components of the complement of a generic wavefront at its singular points.
Bibliography: 22 titles.