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Techniques complexes d'étude d'E.D.O.

D. Cerveau, D. Garba Belko, R. Meziani (2008)

Publicacions Matemàtiques

The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects

Jean Ecalle, Bruno Vallet (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

The characteristic variety of a generic foliation

Jorge Vitório Pereira (2012)

Journal of the European Mathematical Society

We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

The dynamics of holomorphic maps near curves of fixed points

Filippo Bracci (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $M$ be a two-dimensional complex manifold and $f : M \to M$ a holomorphic map. Let $S \subset M$ be a curve made of fixed points of $f$ , i.e. $Fix (f) = S$ . We study the dynamics near $S$ in case $f$ acts as the identity on the normal bundle of the regular part of $S$ . Besides results of local nature, we prove that if $S$ is a globally and locally irreducible compact curve such that $S \cdot S < 0$ then there exists a point $p \in S$ and a holomorphic $f$ -invariant curve with $p$ on the boundary which is attracted by $p$ under the action of $f$ . These results are achieved...

The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms

J. Ecalle, D. Schlomiuk (1993)

Annales de l'institut Fourier

Transversely affine and transversely projective holomorphic foliations

B. Azevedo Scárdua (1997)

Annales scientifiques de l'École Normale Supérieure