Dirichlet series with functional equations and related arithmetical identities
Disconnected Julia set and rotation sets
Distributional and entire solutions of linear functional differential equations.
Distributional and entire solutions of ordinary differential and functional differential equations.
Dynamical behavior of two permutable entire functions
We show that two permutable transcendental entire functions may have different dynamical properties, which is very different from the rational functions case.
Dynamical properties of some classes of entire functions
The paper is concerned with the dynamics of an entire transcendental function whose inverse has only finitely many singularities. It is rpoven that there are no escaping orbits on the Fatou set. Under some extra assumptions the set of escaping orbits has zero Lebesgue measure. If a function depends analytically on parameters then a periodic point as a function of parameters has only algebraic singularities. This yields the Structural Stability Theorem.
Dynamics of entire maps
Dynamics of meromorphic maps : maps with polynomial schwarzian derivative
Dynamics of quadratic polynomials : complex bounds for real maps
We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map , , is locally connected.
Dynamics of transcendental meromorphic functions.
Elementary examples of Loewner chains generated by densities
We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
Ensembles de Julia de mesure positive
Ensembles de Julia et propriétés de localisation des entiers algbériques.
Entropie de l'image inverse d'une application
Ergodicity of some classes of meromorphic functions.
Errata-Corrige : “Iteration theory, compactly divergent sequences and commuting holomorphic maps”
Exact asymptotics of nonlinear difference equations with levels and
We study a class of nonlinear difference equations admitting a -Gevrey formal power series solution which, in general, is not - (or Borel-) summable. Using right inverses of an associated difference operator on Banach spaces of so-called quasi-functions, we prove that this formal solution can be lifted to an analytic solution in a suitable domain of the complex plane and show that this analytic solution is an accelero-sum of the formal power series.
Exceptional values of meromorphic functions and of their derivatives on annuli
This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.
Extraneous Fixed Points, Basin Boundaries and Chaotic Dynamics for Schröder and König Rational Iteration Functions.
Fatou components whose boundaries have a common curve
We show that the Fatou components of a certain transcendental entire function have a common curve in their boundaries.