Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
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
Authors: Şubă Alexandru, Silvia Turuta
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Abstract
In this article, we study the real planar cubic differential systems with a non-degenerate monodromic critical point M 0 . In the cases when the algebraic multiplicity m(Z) = 5 or m(l1) + m(Z) ≥ 5, where Z = 0 is the line at infinity and l1 = 0 is an affine real invariant straight line, we prove that the critical point M0 is of the center type if and only if the first Lyapunov quantity vanishes. More over, if m(Z) = 5 (respectively, m(l1) + m(Z) ≥ 5, m(l1) ≥ j, j = 2,3) then M0 is a center if the cubic systems have a polynomial first integral (respectively, an integrating factor of the form 1/l1j).Vladimir Andrunachievici Institute of Mathematics
and Computer Science
5 Academiei str., Chisinau, MD 2028, Moldova
Tiraspol State University
5 Gh. Iablocichin str., Chisinau, MD-2069, Moldova
E-mail: ,
and Computer Science
5 Academiei str., Chisinau, MD 2028, Moldova
Tiraspol State University
5 Gh. Iablocichin str., Chisinau, MD-2069, Moldova
E-mail: ,
Fulltext
– 0.29 Mb
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
