Skew-product for group-valued edge labellings of Bratteli diagrams.
Sliding mode observers and observability singularity in chaotic synchronization.
Slow and fast systems with Hamiltonian reduced problems.
Small amplitude critical periods in a cubic polynomial system.
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms....
Small perturbations of a discrete twist map
Smooth conjugacy classes of circle diffeomorphisms with irrational rotation number
We prove the C¹-density of every -conjugacy class in the closed subset of diffeomorphisms of the circle with a given irrational rotation number.
Smooth Extensions of Bernoulli Shifts
For homographic extensions of the one-sided Bernoulli shift we construct σ-finite invariant and ergodic product measures. We apply the above to the description of invariant product probability measures for smooth extensions of one-sided Bernoulli shifts.
Smooth Gevrey normal forms of vector fields near a fixed point
We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the “small divisors” are invisible either for the smooth linearization or normal form problem. We prove that this is completely different in the smooth Gevrey category. We prove that a germ of smooth -Gevrey vector field with an hyperbolic linear part admits a smooth -Gevrey transformation to a smooth -Gevrey normal form. The Gevrey order depends on...
Smooth invariant curves of singularities of vector fields on
Smooth linearization of centres
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 models of Thurston's pseudo-Anosov maps
Smooth Non-Bernoulli K-Automorphisms.
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 of invariant density for expanding transformations in higher dimensions.
Smoothness of the attractor of almost all solutions of a delay differential equation [Book]
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...
Snapback Repellers and Semiconjugacy for Iterated Entire Mappings: global aspects of an old Theorem of Poincaré.