Nonlinear Dynamics at the Free University Berlin

Winter 2017/2018

Oberseminar Nonlinear Dynamics



Oct 17, 2017 Jan Sieber
(University of Exeter)
Smooth center manifolds for delay-differential equations
Abstract: Delay-differential equations (DDEs) with state-dependent delays are, as far as is known, at best continuously differentiable once as dynamical systems. That is, the time-t 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 Non-autonomous Systems
We survey the notions of global attractors for non-autonomous systems, and consider small non-autonomous perturbations of dynamical systems to discuss the resulting changes on the global attractors. We review the notion of Morse-Smale dynamical system and extend this notion to the non-autonomous 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 two-dimensional 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 Jia-Yuan 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 periodic-in-space solutions. The idea of the proof is to apply the Lyapunov-Schmidt reduction. We will solve a related small-divisor 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 Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation
We discuss a Gagliardo-Nirenberg-type 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 Gagliardo-Nirenberg-type 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.

Time and Place

Talks usually take place on Tuesday at 3:15 p.m.
at the Free University Berlin
Arnimallee 7 (rear building), room 140.

Tea/coffee at 2:45 p.m.
Arnimallee 3 (rear building), room 136 (kitchen).
Guests are always welcome !


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