Abstract
The singularities of hyperbolic polynomials (hypersurfaces) and the singularities of the boundary of the hyperbolicity region are investigated. Theorems on stabilization of these singularities in families with a fixed number of parameters and on their relationship with elliptic singularities are proved. The problems considered in this study are part of a research program focusing on singularities of boundaries of spaces of differential equations, proposed by V. I. Arnol'd.
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