Holomorphic solutions of functional differential systems near singular points

Straightening out Trajectories near Singular Points of Implicit Differential Equations

Under appropriate assumptions, it is shown that there is a di eomorphism that transforms solutions of the implicit di erential equation

Holomorphic Dynamics near Germs of Singular Curves

Let M be a two dimensional complex manifold, p ∈ M and F a germ of holomorphic foliation of M at p. Let S ⊂ M be a germ of an irreducible, possibly singular, curve at p in M which is a separatrix for F . We prove that if the Camacho-Sad-Suwa index Ind(F , S, p) 6∈ Q ∪ {0} then there exists another separatrix for F at p. A similar result is proved for the existence of parabolic curves for germs ...

A Normal Form for Implicit Differential Equations near Singular Points

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

Singular Solutions and Prolongation of Holomorphic Solutions to Nonlinear Differential Equations

Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points

l=0 |c l | < 1, and xl(z) = x(xl−1(z)) that denote the nth iterate of a map x. In general, F, G are given complex-valued functions of a complex variable. In this paper, analytic solutions of nonlinear iterative functional differential equations are investigated. Existence of locally analytic solutions and their construction is given in the case that all given functions exist regular points. As ...