Nonlinear Dynamics at the Free University Berlin

Winter 2008/2009

Oberseminar Nonlinear Dynamics



Oct 14, 2008 Victor Tkachenko
(Academy of Sciences, Kiev)
Slowly oscillating wave solutions of a single-species reaction-diffusion equation with delay
14:45, Free Unversity Berlin, Arnimallee 7, 14195 Berlin, Room 140
SFB 647
Oct 21, 2008 Alexey Teplinsky
(Academy of Sciences, Kiev)
Smooth conjugacy of circle diffeomorphisms with singularities
Oct 28, 2008 Grigory Bordyugov
(Universität Potsdam)
Response functions of spiral waves
Nov 04, 2008 SFB 647
Nov 11, 2008 Nitsan Ben-Gal
(FUB / Brown University)
Asymptotics of Grow-Up Solutions and Global Attractors of Non-Dissipative PDEs
There has been a great deal of work in recent years on the asymptotics of solutions to scalar parabolic pdes which remain bounded or blow up in finite time. In this talk we will discuss recent results addressing the boundary case of grow-up solutions. These results allow for a thorough understanding of the asymptotics of grow-up solutions and a complete decomposition of the global attractor for the ensuing non-dissipative reaction-diffusion systems.
Nov 18, 2008 Workshop on Complex Dynamics in Large Coupled Systems
Nov 25, 2008 SFB 647
Dec 02, 2008 George R. Sell
(University of Minnesota)
On the theory and applications of the longtime dynamics of 3-dimensional fluid flows on thin domains
The current theory of global attractors for the Navier-Stokes equations on thin 3D domains is motivated by the desire to better understand the theory of heat transfer in the oceans of the Earth. (In this context, the thinness refers to the aspect ratio - depth divided by expanse - of the oceans.) The issue of heat transfer is, of course, closely connected with many of the major questions concerning the climate. In order to exploit the tools of modern dynamical systems in this study, one needs to know that the global attractors are "good" in the sense that the nonlinearities are Frechet differentiable on these attractors.
About 20 years ago, it was discovered that on certain thin 3D domains, the Navier-Stokes equations did possess good global attractors. This discovery, which was itself a major milestone in the study of the 3D Navier-Stokes equations, left open the matter of extending the theory to cover oceanic-like regions with the appropriate physical boundary behavior. In this lecture, we will review this theory, and the connections with climate modeling, while placing special emphasis on the recent developments for fluid flows with the Navier (or slip) boundary conditions.
Dec 09, 2008 Frank Schilder
(University of Surrey)
Computational bifurcation analysis of Hamiltonian relative periodic orbits
Dec 16, 2008 SFB 647
Jan 13, 2009 SFB 647
Jan 20, 2009 Juleitte Hell
(Freie Universität Berlin
Conley Index at Infinity
We interpret blow up phenomena as heteroclinic connections to infinity and propose to analyse them with Conley index methods. To apply those at infinity we have to face two main obstacles: the lack of boundedness of neighbourhoods of infinity and the frequent degenerate behaviour at infinity. The first obstacle may be overcome by "compactification" of the phase space while the second forces us to generalise the definition of the Conley index to a class of degenerate invariant sets at infinity. We show how this new definition fits into the machinery allowing to detect heteroclinic orbits.
Jan 27, 2009 Jens Rademacher
(Centrum Wiskunde & Informatica Amsterdam)
Lyapunov-Schmidt Reduction for Unfolding Heteroclinic Networks of Equilibria and Periodic Orbits with Tangencies
When all nodes in a heteroclinic network are equilibria much is known about the bifurcations. Recently, heteroclinic networks whose nodes can also be periodic orbits have found increasing attention. In the present article we consider finite heteroclinic networks in arbitrary phase space dimensions whose nodes can be an arbitrary mixture of equilibria and periodic orbits. In addition, we allow for tangencies in the intersection of un/stable manifolds. The problem we address is to find solutions that are close to the heteroclinic network for all time, and their parameter values. The main result is a reduction of this problem to a system of algebraic equations for the parameters with leading order expansion in terms of certain geometric characteristics. The only difference for a periodic orbit instead of an equilibrium is that one of these characteristics becomes discrete. The essential assumptions are hyperbolicity of the nodes and transversality of parameter variation.
Feb 03, 2009 SFB 647
Feb 10, 2009 A.L. Skubachevskii
(Moscow State Aviation Institute)
Elliptic functional differential equations with degeneration

Time and Place

Talks usually take place on Tuesday at 3:15 p.m.
at the Weierstraß Institute
Ehrhard-Schmid-Hiörsaal, 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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