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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
