Nonlinear Dynamics at the Free University Berlin

Winter 2011/12

Forschungsseminar Dynamische Systeme

(Seminar for Candidates for Bachelor, Masters, Diploma, Dissertation)

(Internes Seminar der Arbeitsgruppe Nichtlineare Dynamik)

PD Dr. P. Gurevich, Dr. Stefan Liebscher


Oct 20, 2011 Bernhard Brehm
(Freie Universität Berlin)
Measure-theoretic estimates for Bianchi cosmologies
Nov 10, 2011 Stefan Liebscher
(Freie Universität Berlin)
Local passage near the Kasner circle in cosmologial models of Bianchi type with magnetic field
Nov 17, 2011 Abderrahim Azouani
(Freie Universität Berlin)
Feedback control of nonlinear dissipative systems
I will start by reaction-diffusion paradigm to design a feedback control that stabilizes the unstable solution, for example, either by observing the values of the solutions at certain nodal points, local averages of the solutions, or by observing many of their Fourier modes.
Another interesting example is the Navier-Stokes equations. The feedback control is designed in order to force the solution to converge to the steady state solution. An appropriate upper bound N of the determining nodes to stabilize the solutions of the Navier Stokes is derived in terms of Grashof number.
Discrete data assimilation inserts the observational measurements of the reference dynamical system into an approximate solution. I will discuss this idea, which is used to initialize a weather forecasting model.
Nov 24, 2011 Juliette Hell, Alexey Osipov
(Freie Universität Berlin)
Shadowing lemmas and Conley index
Standard shadowing lemma claims that a dynamical system has a shadowing property in a small neighborhood of a hyperbolic set (i.e. in this neighborhood any sufficiently precise ''approximate solution'' is ''close'' to some exact solution). In this talk we will try to look at shadowing from a topological point of view. Our talk will be mostly based on papers of Conley and Easton. We will describe Conley's way of proving standard shadowing lemma, which reduces the problem to studying sequences of mappings of ''squares''. We will speak about Easton's strategy of shadowing pseudotrajectories (i.e. ''approximate solutions'') via ''chains of windows''. Besides, we will discuss possible modifications of this results for a certain non-standard shadowing property, which naturally arises, when one tries to transfer standard shadowing property via compactification/decompactification technique (e.g. Poincare compactification).
Dec 01, 2011 Ernesto Nungesser
(Albert-Einstein-Institute Golm)
Late-time behaviour of the Einstein-Vlasov system with Bianchi symmetry
In the beginning of the talk I will introduce the Einstein equations on a mass shell and the Vlasov equation in the case of Bianchi symmetry. In the second part of the talk I will discuss the methods used to obtain the main results which concern the late-time behaviour assuming small data for certain Bianchi types.
Dec 08, 2011 Ksenia Darovskaya
(Peoples' Friendship University, Moscow)
A priory estimates of solutions for a differential operator with integral conditions
We consider an ordinary differential equation of the second order with a spectral parameter and integral conditions of several types. For each type of conditions, an a priory estimate of solutions for sufficiently large values of the parameter is proved. As a consequence, sufficient conditions of the Fredholm solvability for such problems are obtained.
Dina Kalinichenko
(St. Petersburg State University)
Free boundary two-phase inductive heating problem
The inductive heating process is considered. The free boundary two-phase inductive heating problem is modeled. An application of a small parameter method is discussed.
Dec 15, 2011 Alan Rendall
(Albert-Einstein-Institute Golm)
Multiple steady states in a dynamical system arising in immunology
The subject of this talk is a four-dimensional dynamical system with a large number of parameters modelling certain aspects of the immune system (interaction of T cells and macrophages). The main result is that for certain large subsets of the parameter space this system has at least seven stationary solutions. The method of proof is to guess the position of a stationary solution and then prove the correctness of the guess by a fixed point argument. The steady states which were not previously known represent a possible therapeutic target in the treatment of autoimmune or infectious diseases.
Jan 12, 2012 Lev Lazar
(University of Hamburg)
On conducted and current research of the Neurology of the Visual Perception
Attempts to comprehend the system of visual perception are neither new nor rare. Anyway, the underlying processes are yet to understand. In last twenty years a huge progress is been made in this field by the cooperative work of Biologists, Neurophysicians, Neuropharmacologists, Molecular Biologists, Computer Scientists and Mathematicians.
I'm going to give an overview of research on visual perception and other relevant, tightly related topics. After a brief discussion of involved Neurology and Molecular Biology relevant for understanding (not only from Mathematical point of view) of processes that are finding place in our central nervous system, I'm going to describe the models and concepts purposed to qualitatively analyze the neurology of visual perception, visual cognition and related phenomena.
Jan 17, 2012
Stefan Liebscher
(Freie Universität Berlin)
Invariant manifolds in Maxwell-Bianchi systems
I will concentrate on Lipschitz properties of the local passage near the Kasner circle with respect to a non-standard metric. This yields cone conditions needed for a graph-transformation approach. We obtain unstable manifolds to some Kasner sequences in a more general context than pure Bianchi VIII/IX. This is joint work with Alan Rendall.
Jan 19, 2012 Bernhard Brehm
(Freie Universität Berlin)
More about Bianchi
Jan 26, 2012 Johannes Buchner
(Freie Universität Berlin)
Takens-Linearization for periodic heteroclinic chains in Bianchi IX
Feb 09, 2012 Alexander Nazarov
(St.Petersburg State University)
On the sharp constant in the Poincare inequality with three parameters
In the talk, we discuss the problem of finding a sharp constant in the generalized Poincare inequality. This and some equivalent problems arise in various fields of mathematics. We mention the problem of optimality of some goodness-of-fit criteria in non-parametric statistics and the estimation of critical values in the Lagrange problem. The talk is based on a joint paper with I.V. Gerasimov

Time and Place

Talks usually take place on Thursday at 2:15 p.m.
at the Free University Berlin
Room 130, Arnimallee 3 (rear building), 14195 Berlin.

Guests are always welcome !


switch Last change: Apr. 10, 2012
This page strictly conforms to the XHTMLswitch1.0 standard and uses style sheets. Valid XHTML 1.0! Valid CSS!