Poincaré index of plane polynomial fields of third and fourth degree
https://doi.org/10.29235/1561-2430-2019-55-1-22-31
Abstract
The conditions of isolation of a zero singular point of plane polynomial fields of third and fourth degree are considered in terms of the coefficients of the components of these fields. The isolation conditions depend on the greatest common divisor of the components of polynomial fields: in some cases only on its degree, and in some cases, additionally,
on the presence of nonzero real zeros. The reasoning, which allows one to write out the isolation conditions, is based on the concept of the resultant and subresultants of components of plane polynomial fields. If the zero singular point is isolated, its index is calculated through the values of subresultants and coefficients of components.
About the Authors
P. P. Zabreiko
Belarusian State University.
Belarus
Belarus
Dr. Sc. (Physics and Mathematics), Professor of the Department of Functional Analysis and Analytical Economics, Faculty of Physics and the Faculty of Mathematics.
4, Nezavisimosti Ave., 220030, Minsk.
A. V. Krivko-Krasko
Belarusian State University.
Belarus
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor, Assistant Professor of the Department of Innovation Management, School of Business.
5, Moskovskaya Str., 220007, Minsk.
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