Nonlinear Dynamics at the Free University Berlin

Winter 2010/2011

Oberseminar Nonlinear Dynamics



Sep 28, 2010 Dmitry Glazkov
(University of Yaroslavl, Russia)
Qualitative analysis of one class of optoelectronic systems with singularly perturbed models
1:00 p.m., WIAS, Mohrenstraße 39, 10117 Berlin, Erhard-Schmidt-Hörsaal
Oct 05, 2010 Dmitry Glazkov
(University of Yaroslavl, Russia)
Local dynamics of delay differential equations with long delay feedback
Oct 19, 2010 First German-Russian Interdisciplinary Workshop on the Structure and Dynamics of Matter, BESSY, Albert-Einstein-Straße 15, 12489 Berlin (Program)
Oct 26, 2010 SFB 647
Nov 2, 2010 Carlos Rocha
(Instituto Superior Tecnico, Lisbon, Portugal)
Transversality in scalar reaction-diffusion equations on a circle
Stable and unstable manifolds of hyperbolic periodic orbits for scalar reaction-diffusion equations defined on a circle always intersect transversally. Moreover, hyperbolic periodic orbits do not possess homoclinic orbit connections. We review these results that as main tool use Matano's zero number theory dealing with the Sturm nodal properties of the solutions.
Nov 9, 2010 Flavio Abdenur
(PUC, Rio de Janeiro)
Geometric mechanisms for robust transitivity
A diffeomorphism is said to be robustly transitive if it is transitive, and moreover it is, err, robustly so. (Meaning of course all diffeomorphisms sufficiently close to it are also transitive.) Robustly transitive (but non-Anosov) systems are in a sense a model for non-hyperbolic but hyperbolic-like global behavior. Though many examples have been constructed, and many consequences deduced, the general mechanism(s) that underlie this phenomenon are still poorly understood. I will report on some progress - meaning actual theorems, not just lemmas or tentative ideas - that has been recently achieved in this direction, in the context of partially hyperbolic systems. The exciting keywords here are blenders, minimality of foliations, and the crossing condition. This is a joint (and ongoing) work with Sylvain Crovisier.
Ilya Kashchenko
(University of Yaroslavl, Russia)
Dynamics properties of second-order equations with large delay
(abstract as PDF document)
Nov 16, 2010 SFB 647
Nov 23, 2010 Roman Shamin
(Peoples' Friendship University of Russia,
Shirshov Institute of Oceanology)
Probability of the occurrence of freak waves
Hydrodynamics of ideal heavy liquid with a free surface in conformal variables is studied. In numeric simulations we show occurrence of freak waves. The statistics of the occurrence of freak waves is investigated. The characteristics of freak waves are considered.
Nov 30, 2010 SFB 647
Dec 7, 2010 Martin Väth
(Free University Berlin)
Bifurcation for a Reaction-Diffusion System with Obstacles and Pure Neumann Boundary Conditions
Start at 4:15 p.m., coffee at 3:45 p.m., usual place, see below.
Consider a reaction-diffusion system which is subject to Turing's effect of diffusion-driven instability (leading to patterns). It is known that the presence of obstacles can lead to bifurcation of stationary solutions in a parameter domain where the system is stable (thus amplifying Turing's effect in a sense). However, usually additional Dirichlet conditions were supposed. For almost 30 years it has been an open problem whether the same result holds without Dirichlet conditions. In the talk the somewhat surprising answer is given, and the difficulties of the proof are sketched.
Dec 14, 2010 SFB 647
Jan 11, 2011 SFB 647
Jan 18, 2011 Stefan Liebscher
(Free University Berlin)
Bifurcation without parameters
Jan 25, 2011 Alexander Skubachevskii
(Peoples' Friendship University of Russia)
Damping Problem for Control System with Delay and Nonlocal Boundary Value Problems
We consider damping problem for control system with delay. For the first time this problem was studied by N.N. Krasovskii in 1968 for delay differential equation. We consider the damping problem in general case, i.e. for neutral differential difference equation. Such problem can be formulated as a variational problem for nonlocal functional containing derivatives and shifts for unknown function. We reduce a variational problem to a boundary value problem for a second order neutral differential-difference equation and prove a uniqueness and existence of generalized solution of this boundary value problem. Using a connection between boundary value problem for differential-difference equations and nonlocal boundary value problems we obtain the necessary and sufficient conditions for smoothness of generalized solutions.
Feb 1, 2011 SFB 647

Time and Place

Talks usually take place on Tuesday at 3:15 p.m.
at the Free University Berlin
Room 140, Arnimallee 7 (rear building), 14195 Berlin.

Tea and coffee will be served at 2:45 p.m., Arnimallee 3, Room 006.
Guests are always welcome !


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