Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems.
Authors: Calin Iurie, Baltag Valeriu
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Abstract
The autonomous two-dimensional polynomial cubic systems of differential equations with pure imaginary eigenvalues of the Jacobian matrix at the singular point (0,0) are considered in this paper. The center problem was studied for three classes of such systems: the class of cubic systems with zero divergence of the cubic homogeneities (S 3 ≡ 0), the class of cubic systems with zero divergence of the quadratic homogeneities (S2 ≡ 0) and the class of cubic systems with nonzero divergence of the quadratic homogeneities (S2≢0). For these systems, sufficient GL(2,R)-invariant center conditions for the origin of coordinates of the phase plane were established.Iurie Calin
Vladimir Andrunachievici Institute of
Mathematics and Computer Science
& Moldova State University,
Chisinau, Republic of Moldova
E-mail:
Valeriu Baltag
Vladimir Andrunachievici Institute of
Mathematics and Computer Science
E-mail:
Vladimir Andrunachievici Institute of
Mathematics and Computer Science
& Moldova State University,
Chisinau, Republic of Moldova
E-mail:
Valeriu Baltag
Vladimir Andrunachievici Institute of
Mathematics and Computer Science
E-mail:
Fulltext
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Contents
- Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line
- The problem of the center for cubic differential systems with the line at infinity and an affine real invariant straight line of total algebraic multiplicity five
- The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
- Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations
- The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type (3,3)
- On the upper bound of the number of functionally independent focal quantities of the Lyapunov differential system
- On limit cycles of polynomial systems of the first-order ODEs
- Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems.
- Invariant conditions of stability of unperturbed motion governed by critical differential systems s(1,2,3)
- Working with professor Nicolae Vulpe
