| 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 |
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !
Last change: Jan. 25, 2010
