Geodesic
Singularities of the boundary of a domain of hyperbolicity
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 33 (1988), pp. 193-214
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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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     title = {Singularities of the boundary of a~domain of hyperbolicity},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
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A. D. Vainshtein; B. Z. Shapiro. Singularities of the boundary of a domain of hyperbolicity. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 33 (1988), pp. 193-214. http://geodesic.mathdoc.fr/item/INTD_1988_33_a5/