Techniques complexes d'étude d'E.D.O

We relate some properties of complexifications of real analytic foliations with problems such that existence of first integrals or convergent normalizations. Holomorphic diffeomorphisms having an invariant real foliation play a crucial role

Transformations isotropes des germes de feuilletages holomorphes

AbstractGiven Fω a germ of holomorphic singular foliation at the origin of Cn defined by an equation ω=0 (with ω∧dω=0), we are interested in describing the group of isotropic transformations of Fω, i.e., the group of those germs Φ of diffeomorphisms at the origin of Cn that satisfy Φ∗ω∧ω=0

Transversely projective foliations on surfaces: existence of normal forms and prescription of the monodromy

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this result one obtains a natural way to produce invariants for transversely projective foliations on surfaces. Our second main result says that on projective surfaces one can construct singular transversely projective foliations with prescribed monodromy

On the algebraic invariant curves of plane polynomial differential systems

We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate was already found by D. Cerveau and A. Lins Neto [Ann. Inst. Fourier Grenoble 41, 883-903] in a different way.Comment: 10 pages, Latex, to appear in J.Phys.A:Math.Ge

Overexpression of a Medicago truncatula stress-associated protein gene (MtSAP1) leads to nitric oxide accumulation and confers osmotic and salt stress tolerance in transgenic tobacco

The impact of Medicago truncatula stress-associated protein gene (MtSAP1) overexpression has been investigated in Nicotiana tabacum transgenic seedlings. Under optimal conditions, transgenic lines overexpressing MtSAP1 revealed better plant development and higher chlorophyll content as compared to wild type seedlings. Interestingly, transgenic lines showed a stronger accumulation of nitric oxide (NO), a signaling molecule involved in growth and development processes. This NO production seemed to be partially nitrate reductase dependent. Due to the fact that NO has been also reported to play a role in tolerance acquisition of plants to abiotic stresses, the responses of MtSAP1 overexpressors to osmotic and salt stress have been studied. Compared to the wild type, transgenic lines were less affected in their growth and development. Moreover, NO content in MtSAP1 overexpressors was always higher than that detected in wild seedlings under stress conditions. It seems that this better tolerance induced by MtSAP1 overexpression could be associated with this higher NO production that would enable seedlings to reach a high protection level to prepare them to cope with abiotic stresses

Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.Comment: 25 page