# How to quickly generate a nice hyperbolic element

Presented by:
Emmanuel Breuillard
Date:
Friday 12th May 2017 - 13:30 to 14:30
Venue:
INI Seminar Room 1
Abstract:
In the 60's Rota and Strang defined the notion of joint spectral radius of a finite set of matrices. This adequately generalizes the spectral radius of a single matrix to several matrices, and the relation between the limit norm of powers and the maximal eigenvalue (spectral radius formula) can be extended to this setting. In this talk I will present a general geometric formulation in which one considers a finite set of isometries S and the joint minimal displacement L(S), which is closely related to the joint spectral radius of Rota and Strang. The main result is a spectral radius formula for isometric actions on spaces with non-positive curvature (in particular symmetric spaces of non-compact type and \delta-hyperbolic spaces) which extends the previously known results about matrices. Applications to uniform exponential growth will be given. Joint work with Koji Fujiwara.
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