Workshop on Dynamical Systems and Geometry
Conference date: Friday, Feb 8, 2008
Conference aim and scope:
The goal of this workshop is to unite the Dynamical Systems community in northern Germany.
Geomatikum, University of Hamburg, Germany
Address: Bundesstr. 55, 20146 Hamburg, Germany.
11:00 - 11:05 Roland Gunesch: Greetings, introduction, and opening remarks
11:05 - 11:50 Reiner Lauterbach: Bifurcations from synchrony in homogeneous networks
12:15 - 13:15 Vladlen Timorin: Regluing: topological and conformal
13:15 - 15:00 lunch and scientific discussion
15:00 - 16:00 Marc Keßeböhmer: Hölder irregularity of conjugacy maps
16:30 - 17:30 Keivan Mallahi-Karai: Free sub-semigroups of solvable groups
18:00 - 19:00 Dierk Schleicher: Newton's Method as a Dynamical System for Efficient Root Finding of Complex Polynomials
The talks from 11 to 12 are in lecture hall H4, the talk from 12:15 to
13:15 is in lecture hall H5, and all later talks are in lecture hall
Titles and abstracts:
Free sub-semigroups of solvable groups
In this talk, we will show that dynamics of the affine actions of the line
can be used to prove the existence of Zariski-dense free semi-groups in
connected solvable (and non-nilpotent) groups. This partially generalizes a
theorem of Rosenblatt.
Hölder irregularity of conjugacy maps
Work in progress, jointly with Thomas Jordan, Mark Pollicot, and Bernd Stratmann.
Reiner Lauterbach: Bifurcations from synchrony in homogeneous networks
regular network is a network with one kind of node and one kind of
coupling. We show that a codimension one bifurcation from a synchronous
equilibrium in a regular network is at linear level isomorphic to a
generalized eigenspace of the adjacency matrix of the network, at least
wh en the dimension of the internal dynamics of each node is greater
than 1. We also introduce the notion of a product network---a network
where the nodes of one network are replaced by copies of another
network. We show that generically the center subspace of a bifurcation
in product networks is the tensor product of generalized eigenspaces of
the adjacency matrices of the two networks.
Dierk Schleicher: Newton's Method as a Dynamical System for Efficient Root Finding of Complex Polynomials
We turn Newton's method into a concrete algorithm that
takes as input a degree d complex polynomial and an accuracy epsilon,
and gives as output the d complex roots with precision epsilon, and
estimate the "expected" complexity of this algorithms to be "roughly"
This combines old work jointly with Hubbard and Shishikura with new
Regluing: topological and conformal
Regluing is a topological operation that helps e.g. to construct topological
models for certain rational functions. I will give one explicit example of
regluing showing its conformal meaning.
Roland Gunesch, University of Hamburg
page last modified Feb 07, 2008