Jorge Mozo-Fernández

Tauberian properties for monomial summability with applications to Pfaffian systems

Abstract In this paper we will show that monomial summability processes with respect to different monomials are not compatible, except in the (trivial) case of a convergent series. We will apply this fact to the study of solutions of Pfaffian systems with normal crossings, focusing in the implications of the complete integrability condition on these systems.

An extension of Borel–Laplace methods and monomial summability

Abstract In this paper we will show that monomial summability can be characterized using Borel–Laplace like integral transformations depending of a parameter 0 s 1 . We will apply this result to prove 1-summability in a monomial of formal solutions of a family of partial differential equations.

Recognition of Polynomial Plane Curves Under Affine Transformations

Abstract. We present a new method to decide if two algebraic plane curves are (or are not) affine equivalent. The method is based on describing the curves by means of local parametrizations around related points. To that end we introduce a new type of parametrizations, called Ancochea parametrizations, which are canonical under affine transformations.

Dicritical nilpotent holomorphic foliations

We study in this paper several properties concerning singularities of foliations in \begin{document}

Numeric-symbolic methods for computing the Liouvillian solutions of differential equations and systems

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Multisummability of Formal Solutions of Singular Perturbation Problems

\end{document} that are pull-back of dicritical foliations in \begin{document}

Compounding Secret Sharing Schemes

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On the quasi-ordinary cuspidal foliations in (C 3 , 0) ✩

\end{document} . Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in \begin{document}

On codimension one foliations with prescribed cuspidal separatrix

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STRONG ASYMPTOTIC EXPANSIONS IN A MULTIDIRECTION

\end{document} , the adaptations are not straightforward.