Nonlinear Dynamics at the Free University Berlin

Summer 2011

Forschungsseminar Dynamische Systeme

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

(Internes Seminar der Arbeitsgruppe Nichtlineare Dynamik)

Prof. Dr. Bernold Fiedler

PD Dr. P. Gurevich, Dr. Stefan Liebscher


Apr 14, 2011 Stefan Liebscher
(Freie Universität Berlin)
Fishing for ideas on Bianchi Models
Apr 28, 2011 SFB 910, Opening Colloquium
May 5, 2011 Johannes Buchner
(Freie Universität Berlin)
Towards a convergence result for Bianchi cosmologies of class B
The BKL conjecture suggests that the approach to the initial singularity ("big bang") is vacuum dominated, local and oscillatory. After some results have been achieved in a spatially homogeneous setting of Bianchi class A (Mixmaster-models), the natural next step is to consider Bianchi models of class B.
In my talk, I will deal with the Bianchi VI-1/9-model - the most important one in class B, as it is the only Bianchi model appearing in the simplest osciallatory PDE cosmological models.
I will show that the combined local linear passage near the 3-cycle of the Kasner-circle yields a convergence towards the conjectured Bianchi-attractor. I will then discuss what steps are necessary to turn this into a rigorous convergence theorem, including a detailed study of the global passage between the local passages near the Kasner circle.
May 12, 2011 Sergey Tikhomirov
(Freie Universität Berlin)
Control by hysteresis in reaction-diffusion systems
Hysteresis plays a crucial role in control of artificial systems and those created by nature. In the talk, we discuss how it may lead to periodic regimes and pattern formation in various reaction-diffusion equations.
May 19, 2011 Abderrahim Azouani
(Freie Universität Berlin)
Feedback control of nonlinear dissipative systems. Reaction-diffusion paradigm
The aim of this talk is to design a feedback control that stabilizes an unstable solution of a reaction-diffusion equation, as an example of dissipative evolution equations on the finite-dimensional space, by introducing an approximate interpolant of order h. First, our result is demonstrated for the case of local averages, which is the most straightforward approach. Later, a more general abstract result will be presented that unifies our approach, utilizing all types of approximate interpolant observables and controllers. It will be shown that this abstract approach applies to the Fourier modes and nodal value as particular examples. If we have time, I will present briefly a different feedback control based on nodal value observables and feedback controllers. The observables are the values of the solutions u(xk) while the feedback controllers are at some points xk. Joint work with E.S. Titi (University of California, Weizmann Institute of Science).
May 26, 2011 Pavel Gurevich
(Freie Universität Berlin)
Reaction-diffusion equations with spatially distributed hysteresis
We consider reaction-diffusion equations involving a hysteretic discontinuity which is defined at each spatial point. We call this discontinuity spatially distributed hysteresis. In the talk, we discuss how it naturally appears and which basic properties it possesses. We give a sufficient condition under which the problem is well posed and formulate open questions for further research.
May 31, 2011
Juliette Hell
(Freie Universität Berlin)
Dynamics at Infinity
June 9, 2011 Isabelle Schneider
(Free University Berlin)
Delay stabilization of periodic orbits in coupled oscillator systems
Anna Karnauhova
(Free University Berlin)
On manifolds admitting Anosov diffeomorphisms
Christopher Brandt
(Free University Berlin)
Problems in the proof of the existence of a cascade of period doubling bifurcations
June 16, 2011 Sergey Skopinov
(Saint-Petersburg State University)
Microwave heating
Bernold Fiedler
(Free University Berlin)
Flageolet on the vibrating string: theory and experiments
Flageolet is a very common playing technique on string instruments: the finger touches the string slightly, at integer partitions, to produce a peculiar whistling-like sound. The standard string equation, alias the linear wave equation on the interval, does not accommodate such an effect. I discuss several generalizations, based on qualitative and quantitative experiments on my violin during the talk.
Thanks are due to Stefan Liebscher, for helpful hints on friction, and to Wolfgang Boettcher, for helpful demonstrations on his cello.
June 23, 2011 Sergey Skopinov
(Saint-Petersburg State University)
Boundedness and unboundedness of classical solutions in one-dimensional heating problems
June 30, 2011 Waldyr Muniz Oliva
(Instituto Superior Tecnico, Lisbon, Portugal)
The story of the Lotka-Volterra systems
1. Basic notions on conservative, dissipative and stably dissipative L-V systems.
2. Associated graphs and the Volterra's characterization of conservative systems. Symplectic and Poisson structures, Volterra's direct hamiltonian formulation with the double of variables and the reduction.
3. Stably dissipative L-V systems and the hamiltonian dynamics of the attractor. The reduction of that dynamics to another L-V system with less dimensions.
4. Recent results.
July 1, 2011
Discussion Recent results on Lotka-Volterra systems
July 7, 2011 BCSCCS conference: Engineering of Chemical Complexity
July 14, 2011 Anna KarnauhovaOn Manifolds Admitting Anosov Diffeomorphisms
Vu Xuan TuyenThe global attractor of the sunflower equation
Konstantin BubulzPossibilities of delay stabilization in coupled oscillator systems
Christopher BrandtState of my bachelor thesis on homoclinic bifurcations
Isabelle SchneiderDelay stabilization of periodic orbits in coupled oscillator systems
Matthias BosewitzDelay stabilization of periodic orbits in systems with two coupled oscillators

Time and Place

Talks usually take place on Thursday at 2:15 p.m.
at the Free University Berlin
Room 140, Arnimallee 7, 14195 Berlin.

Guests are always welcome !


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