Jeudi 2 octobre 1997 Séminaire d'analyse numérique et
mécanique, Université de Rennes 1
#
On the joint spectral radius of a family of matrices and applications

## Marino ZENNARO

Department of Mathematical Sciences

Trieste University

Piazzale Europa, 1

34127 Trieste Italy

zennaro@univ.trieste.it
We discuss the problem of stability in difference equations, which
are written in the form
Y_{n}=(A_{0}...A_{n-1})Y_{0}. When
A_{n}= A then the stability is ensured if the spectral radius
of A is strictly less than 1. In the case of variable coefficients the
problem is by far more complicated. Then we need to introduce the
notion of joint spectral radius.