Canonical conjugations at fixed points other than the Denjoy-Wolff point.
Cauchy's functional equation in restricted complex domains.
Characteristic functional equations of polynomials and the Morera-Carleman theorem.
Complex a priori bounds revisited
Complex Analytic and Formal Solutions of Real Analytic Equations in Cn.
Components of degree two hyperbolic rational maps.
Concordant sequences and integral-valued entire functions
A classic theorem of Pólya shows that the function is the “smallest” integral-valued entire transcendental function. A variant due to Gel’fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin’s result together with a further generalization.
Conjugation to a shift and the splitting of invariant manifolds
We give sufficient conditions for a diffeomorphism in the plane to be analytically conjugate to a shift in a complex neighborhood of a segment of an invariant curve. For a family of functions close to the identity uniform estimates are established. As a consequence an exponential upper estimate for splitting of separatrices is established for diffeomorphisms of the plane close to the identity. The constant in the exponent is related to the width of the analyticity domain of the limit flow separatrix....
Conjugations on rotation domains as limit functions of the geometric means of the iterates.
Continuous solutions of a homogeneous functional equation.
Convergence and pre-images of limit points for coding trees for iterations of holomorphic maps.
Convergence des solutions formelles de certaines équations fonctionelles.
Correction to a paper by Newman and Sheingorn.
Correction to the paper "On the continuous dependence of local analytic solutions of a functional equation on given functions''
Corrigendum to "Continuous solutions of a homogeneous functional equation".
Counting rooted trees: the universal law .
Counting walks in a quadrant: a unified approach via boundary value problems
The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations...
Croissance des solutions d'une équation différentielle homogène
Cyclic behavior of linear fractional composition operators.