Nonlinear Dynamics at the Free University Berlin

Summer 2011

Oberseminar Nonlinear Dynamics



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)
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 particles with random initial data. Considering a simplified case of hard-spehere 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 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 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 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 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.
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
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 !


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