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On the Poincaré-Lyapunov constants and the Poincare series

Jaume Giné, Xavier Santallusia (2001)

Applicationes Mathematicae

For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...

On $ω$ -limit sets of nonautonomous differential equations

Boris S. Klebanov (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper the $ω$ -limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of $ω$ -limit sets and a Poincar’e-Bendixon type theorem.

One-parameter family of cubic Kolmogorov system with an isochronous center.

E. Sáez, I. Szántó (1997)

Collectanea Mathematica

We show the existence of a one-parameter family of cubic Kolmogorov system with an isochronous center in the realistic quadrant.

Orbites Hétérocliniques au Voisinage d'une Bifurcation de Poincaré Dégénérée pour les Champs de Vecteurs de ...

René-Louis Clerc, Christian Hartmann, Boniface Razafimandimby (1989)

Monatshefte für Mathematik

Oscillatory properties of some classes of nonlinear differential equations

Milan Medveď (1992)

Mathematica Bohemica

A sufficient condition for the nonoscillation of nonlinear systems of differential equations whose left-hand sides are given by $n$ -th order differential operators which are composed of special nonlinear differential operators of the first order is established. Sufficient conditions for the oscillation of systems of two nonlinear second order differential equations are also presented.