Schedule
The lunch (at noon) of registered participants will be covered by the organisers and will take place
at
Mas de Dardagna.
Monday November 22^{nd} 
9:30  10:30 
John H. Hubbard
Geometric limits: examples and uses in Kleinian Groups and Dynamics, 1/3 
10:45  11:45 
Christiane Rousseau
Germs of analytic families of diffeomorphisms unfolding a parabolic point, 1/3 [PDF]

12:00 
Lunch 
14:45  15:45 
Adam Epstein
Geometric limits in conformal dynamics, 1/3 [PDF]

16:00  17:00 

17:05  18:05 

Tuesday 23^{rd} 
9:30  10:30 
John H. Hubbard
Geometric limits: examples and uses in Kleinian Groups and Dynamics, 2/3 
11:00  12:00 
Adam Epstein
Geometric limits in conformal dynamics, 2/3 
12:30 
Lunch 
15:00  16:00 

16:30  17:30 

Wednesday 24^{th} 
9:30  10:30 
Christiane Rousseau
Germs of analytic families of diffeomorphisms unfolding a parabolic point, 2/3 [PDF]

11:00  12:00 
John H. Hubbard
Geometric limits: examples and uses in Kleinian Groups and Dynamics, 3/3 
12:30 
Lunch 
15:00  16:00 
Adam Epstein
Geometric limits in conformal dynamics, 3/3 
16:30  17:30 
Carsten Lunde Petersen
Double parabolic implosion  Limits of degenerate parabolic quadratic rational maps II 
Thursday 25^{th} 
9:30  10:30 
Christiane Rousseau
Germs of analytic families of diffeomorphisms unfolding a parabolic point, 3/3 [PDF]

11:00  12:00 

12:30 
Lunch 
15:00  16:00 

16:30  17:30 

Abstracts and slides
Ismael Bachy
Limits of closed semigroups of ℂ and application to geometric convergence near a Siegel polynomial.
The space of closed sub semigroups of ℂ* together with the point at infinity has naturally the topology induced by the Hausdorff topology on the space of compact subsets of the Riemann sphere. I will give a description of the closure of the space of one generated sub semigroups. Application : given a polynomial f with a Siegel cycle, a LLC map is a map defined on an open subset of the iterated preimages of the Siegel disk cycle, which takes values in an open subset of the cycle itself and such that for each connected component of its domain, it induces, via the linearizing coordinate, a linear map (depending on the component) between open subsets of the unit disk. I will show that DouadyEpstein enrichments of the dynamic [f] with domain of definition in the iterated preimages of the cycle are precisely LLC maps.
Xavier Buff
Limits of degenerate parabolic quadratic rational maps  I
We investigate the set of quadratic rational maps which possess a degenerate parabolic fixed point.
Arnaud Chéritat
About Inou and Shishikura's near parabolic renormalization
I will explain the first steps in an attempt to define an invariant class under near parabolic renormalization for z^{d}+c.
Files:
Slides/bzoom.mov,
Slides/czoom.mov,
Adam Epstein
Geometric limits in conformal dynamics, 1/3
Luna Lomonaco
Paraboliclike maps
The notion of polynomiallike mappings was introduced by Douady and Hubbard in the groundbreaking paper 'On the dynamics of Polynomial.like mappings' (1985). It has been proven to be instrumental in understanding and solving a host of problems in holomorphic dynamics. A polynomiallike mapping of degree d is naturally characterized by two disjoint subdynamical systems called the internal class and the external class. The external class is a degree d orientation preserving, strongly expanding (hence hyperbolic) covering of the unit circle by itself. We consider a new class of maps similar to polynomiallike mappings but with the external map only weakly expanding, i.e., with parabolic periodic points, and we will call them paraboliclike maps. Since the parabolic periodic points for the external map attract points from the complement of the unit circle, the filled Julia set is not an outward repeller and the domain of such a map can not be relatively compact in the range.
Christopher Penrose
Uniformly continuous conformal metric and equicontinuity for mixed iteration of correspondences
A holomorphic correspondence from the Riemann sphere to itself is defined by an algebraic
equation in two complex variables. When iterated, holomorphic correspondences generalise
rational maps and finitely generated subgroups of PSL(2,ℂ). We consider mixed (forward and
backward) iteration and the question of equicontinuity.
An invariant (admissible) conformal metric is known to exist on the Fatou domains (minus
the grand orbits of attracting periodic cycles) of a rational map and is conjectured to
be uniformly continuous with respect to the spherical metric. Such an invariant conformal
metric is uniformly continuous on "orbicompact" subsets. A similar result holds for a
domain fully invariant under a correspondence where the action lifts to a group resolution.
Christiane Rousseau
Germs of analytic families of diffeomorphisms unfolding a parabolic point, 1/3
Christiane Rousseau
Germs of analytic families of diffeomorphisms unfolding a parabolic point, 2/3
Christiane Rousseau
Germs of analytic families of diffeomorphisms unfolding a parabolic point, 3/3
Mitsuhiro Shishikura
An application of Thurston's theorem on branched coverings
Thurston's theorem is about self branched coverings of 2sphere
and describes when it can be equivalent to a rational map.
His condition involves infinitely many systems of simple closed curves and
in general it is very difficult to check. Previous successful cases are
topological polynomials and mating of quadratic polynomials.
In this talk, we try to give another case which is constructed by plumbing from
a piecewise linear map on a tree. We will see how one can take advantage
of an invariant multicurve which is not a Thurston obstruction.
Wang XiaoGuang
Decompostion of nonparabolic branched covering and characterization of rational maps with Herman rings
The aim of this talk is to generalize Thurston's Theorem to postcritically infinite case, and characterize rational maps with attracting cycles, Siegel disks and Herman rings. Based on Guizhen Cui and Tan Lei's work on characterization of hyperbolic rational maps and Shishikura's HermanSiegel surgery, we show that the combinatorics and rational realization of every nonparabolic branched covering is essentially determined by finitely many Siegel maps or Thurston maps. As an application, we give a characterization of a class of rational maps with Herman ring.