Annales de la Faculté des Sciences de Toulouse

G. Leloup

Autour des groupes cycliquement ordonnés

Arnaud Chéritat

Tan Lei and Shishikura’s example of non-mateable degree 3 polynomials without a Levy cycle

Kevin M. Pilgrim

An algebraic formulation of Thurston’s characterization of rational functions

Mary Rees

ANNALES
DE LA FACULTÉ
DES SCIENCES
Mathématiques
MARY REES
Préface
Tome XXI, no S5 (2012), p. i-i.
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Préface
I first heard about mating of polynomials in 1983, and since it was
Adrien Douady who used the term, I took it to be a joke, or mostly so. But
not many jokes keep their punch for thirty years. Interestingly, I can find
no published reference before Douady’s ICM article in 1986. But by that
time, the research groups of both Douady and Hubbard were engrossed by
this intriguing but problematic outgrowth of the groundbreaking discovery
of the structure of the Mandelbrot set. It is intriguing, because surely the
beautiful, intricate, but natural description of dynamics in the Mandelbrot
set of polynomials must translate into the larger parameter space. Of course
it does, and some of it we know, but it is the problems that have kept all
of us going. Over the last thirty years, as this volume shows, the concept
has permeated complex dynamics, has formed an alliance with the theory of
Kleinian groups, where the concept is of at least equal importance, has mo-
tivated developments, as in iterated monodromy groups, and has attracted
researchers younger than the concept itself.
So what are the problems? On a basic level, there are the twin problems
of realisation of the topological mating structure in parameter space, and
of what is essentially its reverse: recognition of a map in parameter space:
what is described in one article as the constructive or descriptive approach.
Probably examples are the key. Matings are relatively easy to produce. So
if we want to check out a theory, we reach for a mating. Matings provided
the first main application of Thurston’s Theorem, and have provided, and
continue to provide, many important examples. But the links between ex-
ample and theory are more involved, as illustrated here. The iteration on
Teichmüller space which is used to prove Thurston’s Theorem is of at least
comparable importance. It is often said, as is true, that research in complex
dynamics over recent decades has been largely inspired by computer graph-
ics. Nowhere is this more true than for studies of mating. In large part this
is due to Arnaud Cheritat’s now-famous movies of matings, which were a
constant reference point for talks at the 2011 Toulouse workshop in mat-
ings, and which make use of Thurston’s theorem and of recent studies and
applications of it. So we have not just graphics, but motion, and I think it
is this which makes the study of matings so appealing — truly dynamic —
good for another thirty years?
Mary Rees
– i –


Préface

Pascal Remy

Matrices de Stokes-Ramis et constantes de connexion pour les systèmes différentiels linéaires de niveau unique

Philippe Rambour

Abdellatif Seghier

Inversion des matrices de Toeplitz dont le symbole admet un zéro d’ordre rationnel positif, valeur propre minimale

David Ginsbourger

Xavier Bay

Olivier Roustant

Laurent Carraro

Argumentwise invariant kernels for the approximation of invariant functions

Françoise Delon

Introduction

J-M Azaïs

F. Gamboa

B. Iooss

Elżbieta Motyl

Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations

Not a member yet

Autour des groupes cycliquement ordonnés

Tan Lei and Shishikura’s example of non-mateable degree 3 polynomials without a Levy cycle

An algebraic formulation of Thurston’s characterization of rational functions

Préface

Matrices de Stokes-Ramis et constantes de connexion pour les systèmes différentiels linéaires de niveau unique

Inversion des matrices de Toeplitz dont le symbole admet un zéro d’ordre rationnel positif, valeur propre minimale

Argumentwise invariant kernels for the approximation of invariant functions

Introduction

Introduction

Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations

1,744

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