English Intern
Dynamische Systeme und Kontrolltheorie

"cancelled" - Oberseminar "Dynamische Systeme und Kontrolltheorie" - Prof. Dr. Fabian Wirth, Universität Passau

Recent results on the joint spectral radius: Regularity and pseudo-normal forms
Datum: 27.01.2023, 16:00 Uhr
Kategorie: Veranstaltung
Ort: Hubland Nord, Geb. 40, 01.003
Vortragende: Prof. Dr. Fabian Wirth, Universität Passau

Das Seminar wird zu einem späteren Zeitpunkt stattfinden.


This talk is based on joint work with Jeremias Epperlein. In 1960 Rota and Strang defined
the joint spectral radius of a finite set of matrices as the maximal exponential growth rate that
can be attained by arbitrary products from the set. This quantity has found various surprising
results in problems arising from graph theory, analysis and dynamical systems. Many authors
have contributed to our understanding of the joint spectral radius but the theory is still far
from complete. In this talk we will concentrate on two problems: It is already known that
the joint spectral radius is locally Lipschitz continuous as a map from the irreducible, compact
matrix sets. It is conjectured that it is indeed Hoelder continuous on the set of compact matrix
sets induced with the Hausdorff metric. We will report on some progress for this question.
Another question arises concerning to the normal form problem. The joint spectral radius is an
invariant of the action of the general linear group on matrix sets but of course not a complete
invariant. The question is then whether there exists an interesting normal form for this action.
We will discuss a pseudo-normal form and the extended problem on flags, which admits a
simpler representation.