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The transvectants and the integrals for Darboux systems of differential equations.
Authors: Baltag Valeriu, Calin Iurie
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Abstract
We apply the algebraic theory of invariants of differential equations to integrate the polynomial differential systems dx/dt=P1(x,y)+xC(x,y), dy/dt=Q1(x,y)+yC(x,y), where real homogeneous polynomials P1 and Q1 have the first degree and C(x,y) is a real homogeneous polynomial of degree r≥1. In generic cases the invariant algebraic curves and the first integrals for these systems are constructed. The constructed invariant algebraic curves are expressed by comitants and invariants of investigated systems.E-mail: ,
Fulltext
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Contents
- The transvectants and the integrals for Darboux systems of differential equations.
- Open problems on the algebraic limit cycles of planar polynomial vector fields.
- Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four.
- Global Attractors of Quasi-Linear Non-Autonomous Difference Equations.
- Determinantal Analysis of the Polynomial Integrability of Differential Systems.
- Orthogonal Solutions for a Hyperbolic System.
- Two problems from the qualitative theory of Hamiltonian systems (in Russian).
- n-Homogeneous dynamical systems and n-ary algebras.
- Attractors in affine differential systems with impulsive control.
- On theory of surfaces defined by the first order systems of equations.
- Regular maps and quasilinear total differential equations.
- Singularly perturbed Cauchy problem for abstract linear differential equations of second order in Hilbert spaces.
