Summer 2011
Oberseminar Nonlinear Dynamics
Organizers
Program
Apr 19, 2011 
SFB 647 
May 3, 2011 
Sergey Tikhomirov (Free University Berlin) 
Shadowing. State of art and open questions. 
Shadowing theory study properties of approximate trajectories of
homeomorphisms and diffeomorphisms.
This notion is important for stability theory and for
theoretical motivation of numerical simulations.
I give an overview of main results in this theory,
both classical and recent.
As well I will give perspectives for future development in this theory.
The Talk is based on joint works with S. Pilyugin, A.Osipov, K. Palmer. 
May 10, 2011 
SFB 647 
May 17, 2011 
Karsten Matthies (University of Bath) 
Timeevolution of Probability Measures on Collision Trees  a Tool for Micromacro Transitions 
A method is presented to show the validity of continuum
description for the deterministic dynamics of many interacting
particles
with random initial data. Considering a simplified case of
hardspehere
dynamics, where particles are removed after the first collision. We
characterize the many particle flow by collision trees which encode
possible collisions. The convergence of the manyparticle dynamics to
the Boltzmann dynamics is achieved via the convergence of associated
probability measures on collision trees. These probability measures
satisfy nonlinear Kolmogorov equations, which are crucial in the
convergence proof. Joint work with Florian Theil.

May 24, 2011 
Alexey Osipov (St. Petersburg State University) 
Random walks on groups 
We will talk about ''limit behaviour'' of trajectories of random walks on various groups. We will start from simple
examples such as random walks on Z^{2} or Z^{d} for d>2. We will see that almost every trajectory of a random walk
(with nondegenerate measure) on a free nonabelian group converges to the boundary of the free group
(homeomorphic to the Cantor set). Finally, we will consider the case of a random walk on an arbitrary group
that has a normal free nonabelian subgroup (or a normal hyperbolic subgroup).

May 31, 2011 
SFB 647 
June 14, 2011 
Michael Zaks (Humboldt University Berlin) 
A mechanism for birhythmicity in ensembles of coupled oscillators 
June 21, 2011 
SFB 647 
June 28, 2011 
Carlos Rocha (Instituto Superior Tecnico, Lisbon, Portugal) 
Sturm permutations for S^{1}equivariant Sturm attractors 
We consider semilinear parabolic equations of the form u_{t} = u_{xx} + f(u,u_{x})
defined on the circle x ∈ S^{1} = R/2πZ and for dissipative nonlinearity f.
Using the Sturm permutation introduced for the characterization of Neumann flows,
we obtain a characterization for the Sturm attractors A_{f} in this class of problems.
This is based on a joint work with Bernold Fiedler and Mathias Wolfrum.

Sergio Oliva (University Sao Paulo, Brasil) 
Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary 
July 5, 2011 
BCSCCS conference: Engineering of Chemical Complexity 
July 12, 2011 
SFB 647 
Time and Place
Talks usually take place on Tuesday at 3:15 p.m.
at the Weierstraß Institute
EhrhardSchmidHörsaal, Mohrenstr. 39, 10117 Berlin.
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !
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