Oct 17, 2017 
Jan Sieber (University of Exeter) 
Smooth center manifolds for delaydifferential equations 
Abstract: Delaydifferential equations (DDEs) with statedependent delays
are, as far as is known, at best continuously differentiable once as
dynamical systems. That is, the timet map does not depend on its argument
with a higher degree of smoothness than 1. However, as I will show, center
manifolds near equilibria are still as smooth as expected from the spectral
gap and from the smoothness of coefficients. In particular, I will review
what precisely "smoothness of coefficients" means.

Oct 24, 2017 
Carlos Rocha (Instituto Superior Técnico of Lisbon) 
Global Attractors for Nonautonomous Systems 
We survey the notions of global attractors for nonautonomous systems, and consider small nonautonomous perturbations of dynamical systems to discuss the resulting changes on the global attractors. We review the notion of MorseSmale dynamical system and extend this notion to the nonautonomous framework, based on a recent joint work with R. Czaja and W. Oliva.

Nov 7, 2017 
Preparation SFB 910 
Nov 14, 2017 
Preparation SFB 910 
Nov 21, 2017 
Nikita Begun (Saint Petersburg State University) 
Chaos for the saw map 
We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such a map occurs as the Poincare map of simple twodimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as systems with a feedback loop containing the hysteretic stop operator. We analyze chaotic sets and attractors of the ''saw map'' depending on its parameters.

Nov 28, 2017 
Preparation SFB 910 
Dec 5, 2017 
Preparation SFB 910 
Jan 16, 2018 
JiaYuan Dai (Freie Universität Berlin) 
Existence of local solutions of Gowdy spacetimes 
We consider a class of Gowdy spacetimes that reduces the Einstein's field equation to a system of two semilinear wave equations, by assuming a universe without matter, in which the gravitational wave fronts repeat in space and are mutually parallel. To prove the existence of local solutions of the system, we add a linear perturbation and seek periodicinspace solutions. The idea of the proof is to apply the LyapunovSchmidt reduction. We will solve a related smalldivisor problem and discuss how to design the correct functional setting that fits to the nonlinearity.
This ongoing research is a joint work with Dr. Hannes Stuke.

Feb 13, 2018 
Marek Fila (Comenius University, Bratislava) 
A GagliardoNirenbergtype inequality and its applications to decay estimates for solutions of a degenerate parabolic equation

We discuss a GagliardoNirenbergtype inequality for functions with fast decay. We use this inequality to derive upper bounds for the decay rates of solutions of a degenerate parabolic equation. Moreover, we show that these upper bounds, hence also the GagliardoNirenbergtype inequality, are sharp in an appropriate sense.
The talk will consist of two parts  an introduction of one hour and a presentation of proofs of also one hour.
