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Algebraic equations with invariant coefficients in qualitative study of the polynomial homogeneous differential systems. (English)
Authors: Baltag Valeriu
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Abstract
For planar polynomial homogeneous real vector field X=(P,Q) with deg(P) = deg(Q) = n some algebraic equations of degree n+1 with GL(2,R)-invariant coefficients are constructed. A recurrent method for the construction of these coefficients is given. In the generic case each real or imaginary solution si(i=1,2,..., n+1) of the main equation is a value of the derivative of the slope function, calculated for the corresponding invariant line. Other constructed equations have, respectively, the solutions 1/si, 1-si, si/(si - 1), (si-1)/si, 1/(1-si). The equation with the solutions (n+1)si-1 is called residual equation. If X has real invariant lines, the values and signs of solutions of constructed equations determine the behavior of the orbits in a neighbourhood at infinity. If X has not real invariant lines, it is shown that the necessary and sufficient conditions for the center existence can be expressed through the coefficients of residual equation.Institute of Mathematics and Computer Science
Academy of Sciences of Moldova,
5 Academiei str. Chisinau,
MD-2028, Republic of Moldova
E-mail:
Academy of Sciences of Moldova,
5 Academiei str. Chisinau,
MD-2028, Republic of Moldova
E-mail:
Fulltext
– 0.17 Mb
Contents
- Academician C.S.Sibirsky as organizer and head of the Seminar on Qualitative Theory on Differential equations.
- On Strong Stability of Linear Poisson Actions. (English)
- Algebraic equations with invariant coefficients in qualitative study of the polynomial homogeneous differential systems. (English)
- Studying stability of the equilibrium solutions in the restricted Newton's problem of four bodies. (English)
- The centre-focus problem for analytical systems of Lienard form in degenerate case. (English)
- On initial value problem in theory of the second order differential equations. (English)
- About some equations of the third order with six poles. (English)
- On rational bases of GL(2,R)-comitants of planar polynomial systems of differential equations. (English)
- Ergodic sets and mixing extensions of topological transformation semigroups. (English)
- Linear singular perturbations of hyperbolic-parabolic type. (English)
- Numerical investigation of the process of detonation waves interaction with an elastoplastic target. (English)
- Mediateca for the scientists of Moldova: results and prospects. (English)
