Singularities on the boundary of the hyperbolicity region

A. D. Vainshtein, B. Z. Shapiro

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3326-3337
Number of pages12
JournalJournal of Soviet Mathematics
Issue number4
StatePublished - Dec 1990

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Applied Mathematics


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