## CEMAPRE Seminar

### Harmonic limits of dynamical systems

Tobias Wichtrey
(Universität Augsburg)

Abstract: In this talk, we analyze the rotational behaviour of dynamical systems, both in discrete time and in continuous time. With rotational behaviour we mean the existence of rotational factor maps, i.e. semi-conjugations to rotations in the complex plane. In order to analyze this kind of rotational behaviour, we introduce harmonic limits. We discuss the connection between these limits and rotational factor maps, and some properties of the limits, e.g., existence under the presence of an invariant measure by the Wiener Wintner Ergodic Theorem. In the discrete-time case, we investigate the reconstruction of certain phase space partitions via harmonic limits as an application of this theory. As an example for continuous-time systems, we look at linear differential equations (autonomous and periodic), and show the connection between the frequencies of the rotational factor maps and the eigenvalues of the system matrix (or of the Floquet exponents in the periodic case). These concepts can also applied to control systems.

Wednesday, May 12, 2010
Time: 14h30
Room: Sala IAPMEI, Edificio Quelhas, ISEG
http://cemapre.iseg.ulisboa.pt/seminars/cemapre/