Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
Authors: Dana Schlomiuk, Vulpe Nicolae
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Abstract
In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic f(x,y) = 0 and a Darboux invariant of the form f(x,y)λest with λ,s ∈ R and s≠0. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.Dana Schlomiuk
Département de Mathématiques
et de Statistiques Université de Montréal
E-mail:
Nicolae Vulpe
Institute of Mathematics and Computer Science
Academy of Science of Moldova
E-mail:
Département de Mathématiques
et de Statistiques Université de Montréal
E-mail:
Nicolae Vulpe
Institute of Mathematics and Computer Science
Academy of Science of Moldova
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
