Apr 15, 2010 
Gamal Mograby (TUFU Berlin) 
Fractal geometry and applications 
Der Inhalt des Vortrags gliedert sich in vier Themen:

Fraktionale Integration und Differentiation:
Motivation und Definition der RiemannLiouville Integrale.
Eigenschaften wie die Halbgruppeneigenschaft in LpRaume. Beispiel.
Motivation und Definition der RiemannLiouville Ableitungen.
Hinreichende Bedingung fur die Existenz der RiemannLiouville Ableitung.
Keine Vererbung der Halbgruppeneigenschaft, Diskussion an einem Gegenbeispiel.
Beziehungen zwischen der RiemannLiouville Integration und Differentiation.
Weitere Eigenschaften.
Eine geometrische Interpretation des RiemannLiouville Integrals nach Podlubny.
Eine physikalische Interpretation der RiemannLiouville Integrale und Ableitungen nach Podlubny.

Lokale Fraktionale Differentiation:
Motivation und Modifikation der RiemannLiouville Ableitungen.
Definition der lokalen fraktionalen Ableitung.
Analogie zur Interpretation der gewohnlichen Ableitung als "lineare Approximation", anschliessend ein Beispiel.
Weitere Eigeschaften.

Einfuhrung von zum Vortrag relevanten Begriffen aus der Fraktalen Geometrie, wie die Box Dimension.
Methoden zur Berechnung der Box Dimension vom Graph einer Funktion.

Anwendung der lokalen fraktionalen Ableitung in der Fraktalen Geometrie.

Apr 22, 2010 
Stefan Liebscher (FU Berlin) 
Bifurcation without parameters 
Apr 29, 2010 
Kseniya Darovskaya (Peoples' Friendship University, Moscow) 
On a spectral problem with integral conditions 
We consider an ordinary differential operator with a spectral parameter and integral boundary conditions.
An a priori estimate of solutions for sufficiently large values of the parameter is obtained.
Also Fredholm solvability, sectorial structure of the spectrum and its discreteness are proved.

Eyal Ron (FU Berlin) 
A Dynamical Systems Approach to a Uniqueness Problem of a Nonautonomous Planar System 
May 6, 2010 
Stefan Liebscher (FU Berlin) 
The Tumbling Universe: Dynamics of Bianchi Models in the BigBang Limit 
Pavel Gurevich (FU Berlin) 
Dynamics of parabolic equations with hysteresis 
May 20, 2010 
Julia Ehrt (WIAS Berlin) 
Cascades of heteroclinic orbits in hyperbolic balance laws 
Alexey Osipov (St. Petersburg State University) 
Absense of roots of a C^{1}generic diffeomorphism
and the structure of its centraliser 
May 27, 2010 
8th
AIMS Conference on Dynamical Systems, Differential Equations and Applications 
Jun 9, 2010 
Marek Fila (Comenius University, Bratislava) 
(Details on) Homoclinic and Heteroclinic Orbits for a Semilinear Parabolic Equation 
Jun 10, 2010 
Opening symposium of the
Berlin Center for Studies of Complex Chemical Systems 
Jun 17, 2010 
Hans Ringström (KTH Royal Institute of Technology, Stockholm) 
The singularity in the case of T^{3}Gowdy 
Due to the complexity of Einstein's equations, spacetimes
satisfying symmetry conditions are often considered. The simplest
spatially inhomogeneous cosmological solutions arise as a result of
imposing the existence of a 2dimensional group of isometries. The Gowdy
class of spacetimes fall into this category. In the talk, a brief
definition of this class will be given. However, the main focus will be on
the asymptotics in the direction of the singularity; a description of the
behaviour for a generic set of initial data as well as an outline of some
of the arguments used to prove the results will be given.

Jun 24, 2010 
Jens Rademacher (Centrum Wiskunde & Informatica, Amsterdam) 
Mechanisms of semistrong interaction in multiscale reaction diffusion systems 
In spatial multiscale reaction diffusion system where some
diffusion lengths are much shorter than the rest, interfaces can form
where only the components that diffuse on the short scale localize. The
interaction between such interfaces is called semistrong as it is
driven by the nonlocalized components. Cases where the interface motion
is of the order of the square of the short diffusion lengths (second
order) have been studied over the past decade. By formal expansions and
numerical studies we show that the interaction strength can also be of
the same order as the short diffusion length (first order). These
mechanisms are illustrated in the Schnakenberg model and investigate
interaction manifolds and their stability. Taking a model independent
point of view, starting only from a dichotomy in diffusion lengths,
characteristic equations of motion of interfaces for first and second
order semistrong interaction can be derived. For first order pulse
interaction with a single long diffusion length and under certain
natural assumptions several explicit Lyapunovfunctionals such as the
largest interpulse distance are found. This is partly joint work with J.
Ehrt and M. Wolfrum (WIAS, Berlin).

Jul 1, 2010 
Sergio Oliva (University Sao Paulo) 
Reactiondiffusion equations with nonlinear boundary conditions with delays 
We will present some techniques used to pose
reactiondiffusion equations in negative fractional power spaces,
following Dan Henry's book, which can be applied to nonlinear Neumann
boundary conditions. This will then be adapted to study the same
equations but with discrete delays in the reaction term. Finally, we
present a Hopf bifurcation result.

Jul 15, 2010 
Woei Chet Lim (Albert Einstein Institute Potsdam) 
pikes  nonlocal component of the generalized Mixmaster attractor 
In general relativity, dynamics near spacelike singularities
was described by chaotic Mixmaster/BKL oscillation. Spacetimes with two
commuting Killing vector fields exhibit a new phenomenon, namely spikes,
which are subhorizon inhomogeneous structures whose dynamics differs
from BKL dynamics.
I will present some background for Mixmaster oscillation, the generation
of the explicit spike solution using the solutiongenerating
transformation by Rendall and Weaver, and numerical simulations of
spacetimes with two commuting Killing vector fields and
solutionmatching with the explicit spike solution. The numerical
results suggest that the Mixmaster attractor should be generalized to
include the spikes as a nonlocal component.
The last part of this work was done in collaboration with Lars
Andersson, David Garfinkle and Frans Pretorius.
