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On integral conditions for the existence of first integrals analytic saddle singularities
V. León, B. Scárdua
We study one-parameter analytic integrable deformations of the germ of -type complex saddle singularity given by at the origin $0 \in \mathbb C^2\times \mat…
On a theorem of Lyapunov-Poincaré in higher dimension
V. León, B. Scárdua
The classical Lyapunov-Poincaré center theorem assures the existence of a first integral for an analytic one-form near a center singularity in dimension two, provided that the firs…
On singular Frobenius for second order linear partial differential equations
Victor León, Bruno Scárdua
The main subject of this paper is the study of analytic second order linear partial differential equations. We aim to solve the classical equations and some more, in the real or co…
Irreducible holonomy groups and Riccati foliations in higher complex dimension
V. León, M. Martelo, B. Scárdua
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by a similar property of the fundamental group of the complemen…
On the integrability of Hill's equation of the motion of the moon
Fernando Reis, Bruno Scárdua
We study under the standpoint of integrable complex analytic 1-forms (complex analytic foliations), a class of second order ordinary differential equations with periodic coefficien…
Holomorphic plane fields with many invariant hypersurfaces
L. Câmara, B. Scárdua
In this paper we show that a (non necessarily integrable) holomorphic plane field on a compact complex manfold having an infinite number of invariant hypersurfaces must admit a…