Another proof of Borůvka's criterion on global equivalence of the second order ordinary linear differential equations
Appendice à l’article d’Eduardo Corel : Calcul des réseaux de Levelt
Un algorithme est présenté pour calculer en toute généralité le « réseau de Levelt » pour un réseau donné.
Associated linear differential equations to linear second order differential equations of Sturm, Jacobi and general form
Asymptotic behavior of solutions of third order delay differential equations
We give an equivalence criterion on property A and property B for delay third order linear differential equations. We also give comparison results on properties A and B between linear and nonlinear equations, whereby we only suppose that nonlinearity has superlinear growth near infinity.
Asymptotic behaviour of the solutions of a certain type of the third order differential equations
Asymptotic equivalence between two systems of ordinary differential equations
Asymptotic properties of solutions of an -th order nonlinear differential equation with deviating argument
Bifurcation in a model of the population dynamics.
Canonical forms of ordinary linear differential equations
Categorial approach to global transformations of the -th order linear differential equations
Central projections of a pair of accompanying spaces to a linear two-dimensional space of functions with a continuous first derivative
Characterization of several classes of second-order ODEs by using differential invariants.
Connecting fast-slow systems and Conley index theory via transversality.
Continuous dependence on a parameter of solutions of generalized differential equations
Coordinate description of analytic relations
In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.
Covariant constructions in the theory of linear differential equations
Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation...
Decomposition of homogeneous vector fields of degree one and representation of the flow
Decoupling normalizing transformations and local stabilization of nonlinear systems
The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.
Dynamical studies of equations from the Gambier family.