Abstracts of the talks at the
Ph.d. course and workshop Holomorphic
Dynamics  Geometry
of Julia sets in one and more complex variables


The
focus of the Ph.d. course and workshop is on the geometry
of Julia sets in one and more complex variables and the structure of Fatou components in two or more complex variables. The
core of the workshop wil be
a minicourse by Eric Bedford and Han Peters on the structure of Fatoucomponents for Henonmaps. 

Title : Minicourse Fatou
Dynamics of Complex Hénon maps Speakers : Eric Bedford and Han Peters 

Title : : Infinitely
many sinks for residual sets of automorphisms of
low degree in $\C^{3}$ Abstract : Hyperbolic
systems such as Smale's horseshoe were originally
supposed to be dense in the set of parameters in the 1960's. The
discovery in the seventies of the socalled Newhouse's phenomenon, i.e. the
existence of residual sets of diffemorphisms of
compact surfaces with infinitely many sinks ( periodic
attractors ) showed it was false for diffeomorphisms of surfaces. The
technical core of the proof is the reduction to a line of tangency between
the stable and unstable foliations where two Cantor sets must have persistent
intersection. In the
complex setting, this reduction is not possible anymore and to get persistent
homoclinic tangencies and then residual sets of
diffeomorphisms displaying infinitely many sinks, we have to intersect in
fact two Cantor sets in the plane. This was done by Buzzard in 1994 who proved there exists d > 0 such that Newhouse's
phenomenon happens in the space of polynomial automorphisms
of degree greater than d. Bonatti and Diaz introduced a type of horseshoes verifying several
properties they called blender horseshoe. The important property of such
hyperbolic sets lies in the fractal configuration of one of their
stable/unstable manifold which implies persistent intersection between any
well oriented graph and this foliation. They used them to get robust homoclinic tangencies for diffeomorphisms of $\R^{3}$. 

Title
: Singular perturbations of Blaschke products and connectivity of Fatou
components. Title : Periodic Points in nonAutonomous Iteration. 

Title : TBA 

Title
: Convergence properties of the
Thurston algorithm for quadratic matings. Time
permitting, the divergence for Lattes maps and/or convergence of
equipotential gluing is discussed as well.The
latter is an alternative definition of mating, which is based on a holomorphic
motion of polynomial Julia sets. Title
: An implosion
arising from saddle connection in 2D complex dynamics. numerical
pictures show that fiber Julia sets oscillate and behave
discontinuously. This
phenomenon quite resembles the parabolic implosion, and we explain such
behaviors by an analogous
argument as parabolic implosion. This is a joint work with Hiroyuki
Inou. Title : 