Nonlinear Dynamics at the Free University Berlin

Summer 2014

Seminar Advanced Topics in Nonlinear Dynamics

PD Dr. P. Gurevich, Dr. Stefan Liebscher


Apr 24, 2014 Sebastian Eydam
(FU Berlin)
Chaos is cosmological models with scalar fields (introduction to my thesis)
I will give an introduction to the models we are working on, providing a description of the dynamics that will lead to a discrete map. This map is the main focus in my thesis, so I will present some early results of our investigation of it.
Apr 24, 2014 Isabelle Schneider
(FU Berlin)
Equivariant Pyragas control
The general theory of a selective noninvasive feedback control of Pyragas type in the equivariant ODE setting will be discussed.
May 8, 2014 Anna Karnauhova
(FU Berlin)
Construstion of an Anosov diffeomorphism on an infra-nilmanifold
Infra-nilmanifolds are obtained from the group action of an almost-Bieberbach group on a connected simply-connected nilpotent Lie group. After a brief introduction, a tiny mistake in M.Shub's example will be indicated and corrected. Next, the generalization to higher dimensions of the example inspired by M. Shub follows and the talk will be finished by an outlook.
May 15, 2014 Sergey Tikhomirov
(Max Planck Institute for Mathematics in the Science, Leipzig)
Rattling in reaction-diffusion systems with hysteresis
Rehearsal of the SFB talk.
May 15, 2014 Eyal Ron
(FU Berlin)
Controlling the controller: hysteresis-delay differential equations
Rehearsal of the SFB talk.
May 22, 2014 Bernhard Brehm
(FU Berlin)
Oriented Shadowing in Bianchi Class A Cosmologies ("Moscow Rehearsal")
Bianchi Class A cosmological models have been studied extensively as a model for chaotic (oscillatory) curvature blow-up in solutions to the Einstein field equations. This chaos is due to the presence of the so called Mixmaster attractor in the corresponding ODE system. This attractor consists only of heteroclinic trajectories, and exhibits non-uniformly hyperbolic dynamics. Physical heuristics suggest that the behaviour of the system close to the attractor is determined by the behaviour on the attractor (BKL Conjecture). However, rigorous results in this direction are rather sparse. In this talk, we will present a new result in this context, namely that trajectories converging to the attractor are approximated by heteroclinic chains. This theorem and its proof are related to the geometric notion of oriented shadowing.
Jun 5, 2014 Marcone Correa Pereira
(Universidade de Sao Paulo, Sao Paulo, Brazil)
The Neumann problem in oscillating thin domains
In this talk we discuss some recent results about the asymptotic behavior of the solutions of a parabolic problem with homogeneous Neumann boundary conditions posed on thin domains with locally periodic structure on the boundary. We discuss the limit problem dependence with respect to the geometry of the thin domain also studying the convergence of the global attractors. Research partially supported by CNPq 302847/2011-1 and 471210/2013-7, CAPES DGU 267/2008, FAPESP 2008/53094-4 and 2013/22275-1.
Jun 12, 2014 Hannes Stuke
(FU Berlin)
Beyond the blow-up
In this seminar talk I attempt to prove a global continuation result for the nonlinear heat equation in the complex time direction in a special case. This allows to draw some conclusions on the behaviour of the solution near blow-up for example on the blow-up rate and the local profile around the blow up point of the continued solution. If there is still some time left, I will also discuss possible further research directions.
Jun 19, 2014 Bernold Fiedler, Pavel Gurevich, and their groups
(FU Berlin)
Poster rehearsal
We will rehearse our poster presentations for the "SFB-Begutachtung".
Jun 26, 2014 Bernold Fiedler, Pavel Gurevich, and their groups
(FU Berlin)
Poster rehearsal II
We will rehearse our poster presentations for the "SFB-Begutachtung".
Jul 10, 2014 Lmokhtar Ikharrazne
(University Mohammed Premier, National School of Applied Sciences, Al Hoceima, Morocco)
Mathematical and physical aspects of some nonlinear evolution equations
Jul 17, 2014 Students
(FU Berlin)
Overview of students' results

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!


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