12 citations · 57 across the 10 of their papers we have counts for
10 papers
On Bureau's classification of quadratic differential equations in two variables free of movable critical points
Adolfo Guillot
As part of the efforts aimed at extending Painlevé and Gambier's work on second-order equations in one variable to first-order ones in two, in 1981, Bureau classified the systems o…
Foliated affine and projective structures
Bertrand Deroin, Adolfo Guillot
We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations ad…
On the multipliers at fixed points of self-maps of the projective plane
Adolfo Guillot, Valente Ramírez
This paper deals with holomorphic self-maps of the complex projective plane and the algebraic relations among the eigenvalues of the derivatives at the fixed points. These eigenval…
Quadratic Differential Equations in Three Variables without Multivalued Solutions: Part I
Adolfo Guillot
For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multi…
Meromorphic vector fields with single-valued solutions on complex surfaces
Adolfo Guillot
We study ordinary differential equations in the complex domain given by meromorphic vector fields on Kähler compact complex surfaces. We prove that if such an equation has a maxima…
A classification of locally homogeneous affine connections on compact surfaces
Adolfo Guillot, Antonia Sánchez Godinez
We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion…
Quasihomogeneous analytic affine connections on surfaces
Sorin Dumitrescu, Adolfo Guillot
We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally h…
Vector fields, separatrices and Kato surfaces
Adolfo Guillot
We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato…
The geometry of Chazy's homogeneous third-order differential equations
Adolfo Guillot
Chazy studied a family of homogeneous third-order autonomous differential equations. They are those, within a certain class, admitting exclusively single-valued solutions. Each one…
Singular sets of holonomy maps for algebraic foliations
Gabriel Calsamiglia, Bertrand Deroin, Sidney Frankel +1
In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germ…