Singularities on the boundary of the hyperbolicity region

A. D. Vainshtein; B. Z. Shapiro

doi:10.1007/BF01095253

Singularities on the boundary of the hyperbolicity region

A. D. Vainshtein
, B. Z. Shapiro

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3326-3337
Number of pages	12
Journal	Journal of Soviet Mathematics
Volume	52
Issue number	4
DOIs	https://doi.org/10.1007/BF01095253
State	Published - Dec 1990

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/BF01095253

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@article{5f81babb24d24362bc4725bda114d02b,

title = "Singularities on the boundary of the hyperbolicity region",

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.",

author = "Vainshtein, \{A. D.\} and Shapiro, \{B. Z.\}",

year = "1990",

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volume = "52",

pages = "3326--3337",

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T1 - Singularities on the boundary of the hyperbolicity region

AU - Vainshtein, A. D.

AU - Shapiro, B. Z.

PY - 1990/12

Y1 - 1990/12

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0039738066

U2 - 10.1007/BF01095253

DO - 10.1007/BF01095253

M3 - Article

AN - SCOPUS:0039738066

SN - 0090-4104

VL - 52

SP - 3326

EP - 3337

JO - Journal of Soviet Mathematics

JF - Journal of Soviet Mathematics

IS - 4

ER -

Singularities on the boundary of the hyperbolicity region

Abstract

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