Oberseminar Nonlinear Dynamics
|Apr 19, 2011
|May 3, 2011
(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
|May 17, 2011
(University of Bath)
|Time-evolution of Probability Measures on Collision Trees - a Tool for Micro-macro Transitions
A method is presented to show the validity of continuum
description for the deterministic dynamics of many interacting
with random initial data. Considering a simplified case of
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 many-particle 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
(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 Z2 or Zd for d>2. We will see that almost every trajectory of a random walk
(with nondegenerate measure) on a free non-abelian 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 non-abelian subgroup (or a normal hyperbolic subgroup).
|May 31, 2011
|June 14, 2011
(Humboldt University Berlin)
|A mechanism for birhythmicity in ensembles of coupled oscillators
|June 21, 2011
|June 28, 2011
(Instituto Superior Tecnico, Lisbon, Portugal)
|Sturm permutations for S1-equivariant Sturm attractors
We consider semilinear parabolic equations of the form ut = uxx + f(u,ux)
defined on the circle x ∈ S1 = 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 Af in this class of problems.
This is based on a joint work with Bernold Fiedler and Mathias Wolfrum.
(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
Time and Place
Talks usually take place on Tuesday at 3:15 p.m.
at the Weierstraß Institute
Ehrhard-Schmid-Hörsaal, Mohrenstr. 39, 10117 Berlin.
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !