Standard

Two-dimensional homogeneous cubic systems: Classification and normal forms: III. / Basov, V.V.; Chermnykh, A. S. .

In: Vestnik St. Petersburg University: Mathematics, Vol. 50, No. 2, 2017, p. 97-110.

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

Harvard

Basov, VV & Chermnykh, AS 2017, 'Two-dimensional homogeneous cubic systems: Classification and normal forms: III', Vestnik St. Petersburg University: Mathematics, vol. 50, no. 2, pp. 97-110. <https://link.springer.com/article/10.3103/S1063454117020029>

APA

Basov, V. V., & Chermnykh, A. S. (2017). Two-dimensional homogeneous cubic systems: Classification and normal forms: III. Vestnik St. Petersburg University: Mathematics, 50(2), 97-110. https://link.springer.com/article/10.3103/S1063454117020029

Vancouver

Basov VV, Chermnykh AS. Two-dimensional homogeneous cubic systems: Classification and normal forms: III. Vestnik St. Petersburg University: Mathematics. 2017;50(2):97-110.

Author

Basov, V.V. ; Chermnykh, A. S. . / Two-dimensional homogeneous cubic systems: Classification and normal forms: III. In: Vestnik St. Petersburg University: Mathematics. 2017 ; Vol. 50, No. 2. pp. 97-110.

BibTeX

@article{2db821d945284a38b161d275b6ec00e5,
title = "Two-dimensional homogeneous cubic systems: Classification and normal forms: III",
abstract = "This article is the third in a series of works devoted to two-dimensional homogeneous cubic systems. It considers the case where the homogeneous polynomial vector on the right-hand side of the system has a quadratic common factor with real zeros. The set of such systems is divided into classes of linear equivalence, in each of which a simplest system being a third-order normal form is distinguished on the basis of appropriately introduced structural and normalization principles. In fact, this normal form is determined by the coefficient matrix of the right-hand side, which is called a canonical form (CF). Each CF is characterized by an arrangement of nonzero elements, their specific normalization, and a canonical set of admissible values of the unnormalized elements, which ensures that the given CF belongs to a certain equivalence class. In addition, for each CF, (a) conditions on the coefficients of the initial system are obtained, (b) nonsingular linear substitutions reducing the right-hand side of a system satisfying these conditions to a given CF are specified, and (c) the values of the unnormalized elements of the CF thus obtained are given.",
keywords = "homogeneous cubic system, normal form, canonical form",
author = "V.V. Basov and Chermnykh, {A. S.}",
year = "2017",
language = "English",
volume = "50",
pages = "97--110",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Two-dimensional homogeneous cubic systems: Classification and normal forms: III

AU - Basov, V.V.

AU - Chermnykh, A. S.

PY - 2017

Y1 - 2017

N2 - This article is the third in a series of works devoted to two-dimensional homogeneous cubic systems. It considers the case where the homogeneous polynomial vector on the right-hand side of the system has a quadratic common factor with real zeros. The set of such systems is divided into classes of linear equivalence, in each of which a simplest system being a third-order normal form is distinguished on the basis of appropriately introduced structural and normalization principles. In fact, this normal form is determined by the coefficient matrix of the right-hand side, which is called a canonical form (CF). Each CF is characterized by an arrangement of nonzero elements, their specific normalization, and a canonical set of admissible values of the unnormalized elements, which ensures that the given CF belongs to a certain equivalence class. In addition, for each CF, (a) conditions on the coefficients of the initial system are obtained, (b) nonsingular linear substitutions reducing the right-hand side of a system satisfying these conditions to a given CF are specified, and (c) the values of the unnormalized elements of the CF thus obtained are given.

AB - This article is the third in a series of works devoted to two-dimensional homogeneous cubic systems. It considers the case where the homogeneous polynomial vector on the right-hand side of the system has a quadratic common factor with real zeros. The set of such systems is divided into classes of linear equivalence, in each of which a simplest system being a third-order normal form is distinguished on the basis of appropriately introduced structural and normalization principles. In fact, this normal form is determined by the coefficient matrix of the right-hand side, which is called a canonical form (CF). Each CF is characterized by an arrangement of nonzero elements, their specific normalization, and a canonical set of admissible values of the unnormalized elements, which ensures that the given CF belongs to a certain equivalence class. In addition, for each CF, (a) conditions on the coefficients of the initial system are obtained, (b) nonsingular linear substitutions reducing the right-hand side of a system satisfying these conditions to a given CF are specified, and (c) the values of the unnormalized elements of the CF thus obtained are given.

KW - homogeneous cubic system

KW - normal form

KW - canonical form

M3 - Article

VL - 50

SP - 97

EP - 110

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 35254282