Fixed points of composite entire and quasiregular maps.
Fixed points of polynomial maps. I. Rotation subsets of the circles
Fixed points of polynomial maps. Part II. Fixed point portraits
Fonction de Tschakaloff et fonction q-exponentielle
Four different unknown functions satisfying the triangle mean value property for harmonic polynomials, II
Fraktální geometrie
Fundamental solutions for meromorphic linear difference equations in the complex plane, and related problems.
Funktionalgleichungen für konstante Funktionen.
Further extending results of some classes of complex difference and functional equations.
Geometry of the locus of polynomials of degree 4 with iterative roots
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Graphs and functional equations.
Green functions on self-similar graphs and bounds for the spectrum of the laplacian
Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...
Hausdorff convergence and the limit shape of the unicorns.
Holomorphic solutions of an inhomogeneous Cauchy equation.
Hyperbolic components of polynomials with a fixed critical point of maximal order
Hyperbolic components of the complex exponential family
We describe the structure of the hyperbolic components of the parameter plane of the complex exponential family, as started in [1]. More precisely, we label each component with a parameter plane kneading sequence, and we prove the existence of a hyperbolic component for any given such sequence. We also compare these sequences with the more commonly used dynamical kneading sequences.
Hypertranscendency of conjugacies in complex dynamics.
Immediate and Virtual Basins of Newton’s Method for Entire Functions
We investigate the well known Newton method to find roots of entire holomorphic functions. Our main result is that the immediate basin of attraction for every root is simply connected and unbounded. We also introduce “virtual immediate basins” in which the dynamics converges to infinity; we prove that these are simply connected as well.
Indépendance linéaire des valeurs des solutions transcendantes de certaines équations fonctionnelles II
Indice d'un opérateur différentiel