Singularities of vector fields
Smoothness property for bifurcation diagrams.
Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with the line...
Stability and attractivity of solutions of differential equations with impulses at fixed times.
Stability of nonlinear systems under constantly acting perturbations.
Strategies for computation of Lyapunov exponents estimates from discrete data
The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed...
Structural stability and generic properties of planar polynomial vector fields.
Structural stability of classical lattices in one dimension
Structural stability of linear discrete systems via the exponential dichotomy
Structural stability of polynomial second order differential equations with periodic coefficients.
Sur le calcul de la partie principale d'un tore de bifurcation pour un système différentiel périodique
Surstabilité pour une équation différentielle analytique en dimension un
En rapport avec le problème du retard a la bifurcation, la notion de solution surstable est définie pour une famille d’équations différentielles analytiques avec un petit paramètre. Un théorème d’existence des solutions surstables est démontré pour des valeurs exceptionnelles d’un paramètre de contrôle. L’outil principal de la démonstration est un théorème de sommation qui constitue une généralisation d’un résultat de A. I. Neishtadt.