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.