Saddle-focus singular cycles and prevalence of hyperbolicity
Second order linear differential systems
Separatrix conditions yielding either periodic orbits or unusual behavior for flows on M3.
Separatrix conditions yielding either periodic orbits or unusual behavior for flows on M3. (Short Communication).
Singularities of Vector Fields on the Plane With Pointed Direction.
Smooth invariant curves of singularities of vector fields on
Smooth linearization of germs of -actions and holomorphic vector fields
The paper contains a generic condition permitting the linearization in class , , of germs of singular infinitesimal -actions on and of singular holomorphic...
Smooth normalization of a vector field near a semistable limit cycle
We establish a polynomial normal form for a vector field having a limit cycle of multiplicity 2. The smooth classification problem for such fields is closely related to the problem of classification of germs , , solved by F. Takens in 1973. Such germs appear as the germs of Poincaré return maps for semistable cycles, and a smooth conjugacy between any two such germs may be extended to a smooth orbital equivalence between the original fields.If one deals with smooth conjugacy of flows rather than...
Smooth transformations of intervals
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...
Solutions périodiques de systèmes hamiltoniens
Solutions with minimal period for hamiltonian systems in a potential well
Some perturbation results for non-linear problems
We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.
Spectrum of the Poincaré Map for Periodic Reflecting Rays in Generic Domains.
Stability of fixed points for order-preserving discrete-time dynamical systems.
Stable intersections of Cantor sets and homoclinic bifurcations
Stochastic behavior above Feigenbaum's parameter value
Subharmonics of convex non-coercive Hamiltonian systems.
Sur l'équation aux différences affine du premier ordre unidimensionnelle
On étudie les phénomènes de retard à la bifurcation et de butée pour des systèmes discrets lents-rapides du plan. On donne une explication géométrique de ces phénomènes basée sur l’examen de fonctions reliefs. On démontre ensuite l’existence et la vie brève des longs canards, qui sont des trajectoires ne présentant pas de butée. Trois exemples illustrent ces phénomènes. Le premier expose la problématique, le second permet une expérimentation de l’étude théorique sur les longs canards, le troisième...
Symbolic dynamics and geodesic flows