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We enumerate the local Petrovskii lacunas (that is, the domains of localregularity of the principal fundamental solutions) of strictly hyperbolic PDE'swith constant coefficients in $R^N$ at the parabolic singular points of theirwavefronts. These points form the next difficult family of classes of thenatural classification of singular points after the so-called simplesingularities, studied previously.  Also we promote a computer program counting for topologically differentmorsifications of critical points of smooth functions, and hence also for localcomponents of the complement of a generic wavefront at its singular points.

Local Petrovskii lacunas at parabolic singular points of wavefronts of strictly hyperbolic PDE's