KAM theory in configuration space.
Local density of diffeomorphisms with large centralizers
Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Non linearizable holomorphic dynamics having an ancountable number of symmetries.
Normal forms and bifurcations of some equivariant vector fields
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the principle of stability of invariance of physical systems
Orbifold-Uniformizing Differential Equations.
Orbifold-Uniformizing Differential Equations. III. Arrangements Defined by 3-Dimensional Primitive Unitary Reflection Groups.
Persistence of invariant manifolds for perturbations of semiflows with symmetry.
Remarks on the Symmetry lie Algebras of first Integrals of Scalar third Order Ordinary Differential Equation with Maximal Symmetry
Renormalization of cocycles and linear ODE with almost-periodic coefficients.
Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces
We present a scheme for constructing various Conley indices for locally defined maps. In particular, we extend the shape index of Robbin and Salamon to the case of a locally defined map in a locally compact Hausdorff space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativity property of the fixed point index.
Solving the quintic by iteration in three dimensions.
Some new results in state space decoupling of multivariable systems. I. A link between geometric approach and matrix methods
Some new results in state space decoupling of multivariable systems. II. Extensions to decoupling of systems with and output feedback decoupling
Sur l'invariance topologique de la classe de Godbillon-Vey
L’invariant de Godbillon-Vey, classiquement défini pour les feuilletages de classe , peut aussi se définir pour les feuilletages de classe par morceaux. Nous montrons que, dans cette catégorie étendue, l’invariant de Godbillon-Vey n’est pas invariant par conjugaison topologique.
Sur un théorème de Dulac
Nous considérons les champs de vecteurs analytiques de de partie linéaire diagonale non nulle et dont les valeurs propres vérifient des relations de résonances toutes engendrées par une seule relation pour un certain vecteur non nul. Nous montrons que, dans un système de coordonnées locales holomorphes au voisinages de , de tels champs de vecteurs se “mettent" sous une forme normale partielle, tout en exhibant des variétés invariantes, si l’on fait une hypothèse de petits diviseurs diophantiens....
Symmetries and constants of the motion for dynamics in implicit form
The bifurcation set for the resonance problem.
The Conley index for flows preserving generalized symmetries
Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.