Flows and diffeomorphisms.
Flows near compact invariant sets. Part I
It is proved that near a compact, invariant, proper subset of a C⁰ flow on a locally compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. Theorem 1 shows that the connectedness of the phase space implies the existence of a considerably deeper classification of topological flow behaviour in the vicinity of compact invariant sets than that described in the classical theorems of Ura-Kimura and Bhatia. The proposed classification brings...
Flows on supporting all links as orbits.
Flows with cyclic winding numbers groups.
Flows with Periodic Factors on Homogenous Spaces.
Free fall motion in an invariant field of forces: the 2D-case.
From the theorem of Ważewski to computer assisted proofs in dynamics
Generalized Weierstrass ...-functions and KP flows in affine spaces.
Generic observability of dynamical systems.
Geometrical and topological structure of magnetic fields generated by rectilinear wires.
Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem.
Global stability of dynamic systems of high order.
Heat flow of p-harmonic maps with values into spheres.
Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows
Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.
Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.
Integral equations and exponential trichotomy of skew-product flows.
Invariant manifolds associated to invariant subspaces without invariant complements: a graph transform approach.
Invariants of twist-wise flow equivalence.
Jet geometrical extension of the KCC-invariants.
La décomposition dynamique et la différentiabilité des feuilletages des surfaces
Soit un feuilletage singulier d’une surface compacte . Pour analyser la dynamique de , on décompose de façon canonique en sous-surfaces bordées par des courbes transverses à : les composantes de la récurrence de (ensembles quasiminimaux) sont contenues dans les “régions de récurrence” et peuvent être étudiées séparément; par contre dans les autres régions, dites “régions de passage”, la dynamique est triviale. On propose ensuite une définition des feuilletages singuliers de classe sur...