Nonlinear Dynamics at the Free University Berlin

Summer 2009

Oberseminar Nonlinear Dynamics



Apr 21, 2009 Nicolas Roy
(Humboldt University Berlin)
A microlocal approach to Ruelle resonances of Anosov diffeomorphisms
If f is an Anosov diffeomorphism on a compact manifold, the decay of the dynamical correlation functions is governed by the so-called Ruelle resonances. It follows from the works of Baladi & al and Liverani & al, that these resonances can be obtained by a suitable spectral analysis of the composition operator (or another one related to it) called the "Transfer operator".
In this talk, we will show how these results can be obtained by a systematic microlocal analysis, and method coming originaly from Quantum mechanics.
The talk is based on the recent paper: [Faure, Roy, Sjoestrand] "Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances". Open Math. Journal (2008), vol. 1, 35--81.
Apr 28, 2009 SFB 647
May 12, 2009 SFB 647
May 19, 2009 Workshop on Nonlinear Optics in Guided Geometries (WIAS)
May 26, 2009 Leonid Rossovskii
(Peoples' Friendship University of Russia)
Boundary-value problems connected with the pantograph equation and their elliptic analogs
Elliptic functional differential equations with contracted and expanded arguments in the senior terms will be considered. The equations share some principal features with their prototype, the pantograph equation, which possesses a large number of applications in applied mathematics and engineering. Compared to the relatively well studied differential-difference equations, these equations represent diverse mathematical structures and pose different mathematical challenges. We will discuss necessary and sufficient conditions for the Garding inequality, solvability and regularity of solutions to boundary value problems in Sobolev and weighted spaces.
June 02, 2009 SFB 647
June 09, 2009 Markus Dahlem
(Technical University Berlin)
Modeling dynamics in large scale neural populations
June 11, 2009 EHRENKOLLOQUIUM anlässlich des 70. Geburtstages von Klaus R. Schneider
16:15, Berlin-Adlershof, Rudower Chaussee 25 (John-von-Neumann-Haus), Humboldt-Kabinett (1. Etage)
Jan Sieber
(University of Portsmouth)
Using feedback control to find unstable phenomena in experiments
June 16, 2009 Reiner Lauterbach
(University of Hamburg)
Bifurcation in Homogeneous Networks: Linear Theory
In this talk we investigate the tensor product structure of the flow on homogeneous networks. We show that this structure has strong implications on the notion of genericity in networks and we find that the dimension of the internal dynamics is crucial for this. Generically center subspaces are linearly isomorphic to generalized eigenspaces of the adjacency matrix if this dimension is at least 2. This relates to genericity results in equivariant bifurcation theory, where the kernels are generically absolutely irreducible group representations. In equivariant bifurcation theory fixed point spaces play an important role. In the case of networks a similar role is played by colorings of an associated graph and corresponding flow invariant spaces. Finally we present some bifurcation results which generalize the Equivariant Branching Lemma to our situation.
June 23, 2009 SFB 647
June 30, 2009 Julia Ehrt
(Weierstrass Institute Berlin)
Cascades of heteroclinics in hyperbolic balance laws
The talk will focus on the question of global attractors for viscous balance laws and their hyperbolic limit. I will present a result concerning uniqueness of heteroclinic connections in the hyperbolic case and present a corrected result of Fan and Hale's theorem on persistence of heteroclinic connections for vanishing viscosity. Some consequences of this will be discussed.
July 07, 2009 Thomas Lorenz
(University of Frankfurt)
Mutational Analysis - the Cauchy problem in and beyond vector spaces
Thomas Lorenz: Mutational Analysis, 2009 (Habilitationsschrift)
Thomas Lorenz: Mutational Analysis, 2009 (Presentation, Berlin)
July 14, 2009 SFB 647
July 21, 2009 Weierstraß Institute, Ehrhard-Schmid-Hiörsaal, Mohrenstr. 39, 10117 Berlin
Andrey Shilnikov Multistability in models of center pattern generators
We study polyrhythmic dynamics in inhibitory-excitatory models of central pattern generators controlling various locomotive behaviors. We analyze various configurations of CPG motifs and describe the universal mechanisms for synergetic bursting patterns.

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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