Das Existenzproblem multivalenter Lösungen bei Differentialgleichungen.
Decomposition of -adic meromorphic functions
Déformation J-équivalente de polynômes géometriquement finis
Any geometrically finite polynomial f of degree d ≥ 2 with connected Julia set is accessible by structurally stable sub-hyperbolic polynomials of the same degree. Moreover, they are topologically conjugate to f on their Julia sets.
Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps: geometric coding trees technique
We prove that if A is a basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then the periodic points in the boundary of A are dense in this boundary. To prove this in the non-simply connected or parabolic situations we prove a more abstract, geometric coding trees version.
Développements asymptotiques -Gevrey et séries -sommables
Nous donnons une version -analogue de l’asymptotique Gevrey et de la sommabilité de Borel, dues respectivement à G. Watson et E. Borel et systématiquement développées depuis une quinzaine d’années par J.-P. Ramis, Y. Sibuya, etc. Le but de ces auteurs était l’étude des équations différentielles dans le champ complexe. De même notre but est l’étude des équations aux -différences dans le champ complexe, dans la ligne de G.D. Birkhoff et W.J. Trjitzinsky.Plus précisément, nous introduisons une nouvelle...
Die allgemeine Lösung einer zylindrischen Differentialgleichung vierter Ordnung nullten Parameterwertes
Diffusion to infinity for periodic orbits in meromorphic dynamics
A small perturbation of a rational function causes only a small perturbation of its periodic orbits. We show that the situation is different for transcendental maps. Namely, orbits may escape to infinity under small perturbations of parameters. We show examples where this "diffusion to infinity" occurs and prove certain conditions under which it does not.
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.