## Bodo Werner: Research Project## Invariant Curves, Circle Maps and their Numerical Analysis. |

** Discretization of circle maps ** (with N. Nicolaisen),
Z. angew. Math. Phys. 49 (1998) 869-895
Here the Frobenius-Perron operator is discretized by some finite partition of
the circle which leads to a transition matrix representing a
finite Markov chain. The aim is to obtain characteristics
of the circle map by its transition matrix.

In the paper

** The spectrum of the Frobenius-Perron operator
and its discretization for circle diffeomorphisms ** (with
N. Lehmkuhl and W. Hotzel), Hamburger Beiträge zur Angewandten
Mathematik, Reihe A, Preprint 160, January 2001 *File:* hbam2001a160.ps.gz

we ask what information about the dynamic can be obtained from the spectrum.

Two doctorate students are working on this project, Nicole Lehmkuhl and Wernt Hotzel.