Complex ODEs, singularity theory and dynamics

Modifications; resolution of singularities (complex-analytic aspects) (32S45) Singularities of holomorphic vector fields and foliations (32S65) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Cites Work

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Separatrices for $\mathbb{C}^2$ actions on 3-manifolds
Almost étale resolution of foliations
Uniformizing complex ODEs and applications
Recurrent orbits of subgroups of local complex analytic diffeomorphisms
Discrete orbits, recurrence and solvable subgroups of Diff $(\mathbb {C}^2, 0)$
Reduction of singularities of three-dimensional line foliations
Resolution of singularities of real-analytic vector fields in dimension three
Semicompleteness of homogeneous quadratic vector fields
A note on integrability and finite orbits for subgroups of $\mathrm{Diff}(\mathbb C^n,0)$
2-dimensional Lie algebras and separatrices for vector fields on $(\mathbb{C}^3, 0)$
Quadratic forms and holomorphic foliations on singular surfaces
Algebraic solutions of one-dimensional foliations
Equations de Pfaff algébriques
Invariant varieties through singularities of holomorphic vector fields
Existence d'une intégrale première méromorphe pour des germes de feuilletages a feuilles fermées du plan complexe. (Existence of a meromorphic first integral for the germs of foliations with closed leaves in the complex plane)
Desingularization of non-dicritical holomorphic foliations and existence of separatrices
Hypersurfaces solutions d'une équation de Pfaff analytique
Frobenius avec singularites. I: Codimension un
The topology of holomorphic flows with singularity
Minimal, rigid foliations by curves on $\mathbb C\mathbb P^n$
Singularités des flots holomorphes. II. (Singularities of holomorphic flows. II.)
Surfaces of the class VII$_0$ admitting a vector field
Germs of holomorphic vector fields in $\mathbb{C}^ 3$ without a separatrix
Singularités des flots holomorphes. (Singularities of holomorphic flows.)
Pairs of foliations and Mattei-Moussu's theorem
On the equations of Halphen and $\mathrm{SL}_{2}(\mathbb C)$-actions
Equivalence and semi-completude of foliations
Reduction of the singularities of codimension one singular foliations in dimension three
Holonomy and equivalence of analytic foliations
Generic pseudogroups on $( \mathbb{C} , 0)$ and the topology of leaves
REMARKS ON THE ORBITAL ANALYTIC CLASSIFICATION OF GERMS OF VECTOR FIELDS
Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
Semi-complete vector fields of saddle-node type in $\mathbb {C}^n$
A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
Holonomie et intégrales premières
Holomorphic Flows in C 3 , 0 with Resonances
Quand deux sous-variétés sont forcées par leur géométrie à se rencontrer
On the resolution of singularities of one-dimensional foliations on three-manifolds
Basic Algebraic Geometry 1
Cyclic stabilizers and infinitely many hyperbolic orbits for pseudogroups on
Topological aspects of completely integrable foliations
Reduction of Singularities of the Differential Equation Ady = Bdx
A remark on first integrals of vector fields
Singularities of holomorphic vector fields in dimensions $\geq 3$: results and problems

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