Résumé : In this talk I will present several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\’c-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates $U_n$ of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values $p_n$ such that $d(p_n,\partial U_n)\to 0$ as $n\to \infty$. We also prove that if $U_n \cap P(f)=\emptyset$ and the postsingular set of $f$ lies at a positive distance from the Julia set (in $C $) then any sequence of iterates of wandering domains must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values.
(joint work with K. Baranski, X. Jarque and B. Karpinska)
Lieu : salle 207, bat 1R2
Résumé : A Comparative study between algebraic structures for a goal-oriented efficiency in Scientific Computing.
Scientific modelling for industrial prospects relies on revealing the organisation of data coming from physical measurements.
There often exist several different mathematical structures which enable to describe a same problem.
But these structures may provide computations with diverging numerical properties, e.g. quaternions vs matrices to describe successive rotations. How to guide the user who has to choose from a wide range of possible computing frames?
In this talk we consider many frames which are popular in weakly interacting group of scientists.
We propose a comparison of their efficiency to handle the characteristics of the computation (behaviour of structures near singularities, accuracy, complexity, nonlinearities, speed, memory size,… ).
These ideas are exemplified in physical applications.
Lieu : Manufacture des Tabacs bat C 1er étage salle MC101 - 21 Allees de Brienne