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arXiv · 1804.00748

On the joint spectral radius for isometries of non-positively curved spaces and uniform growth

Emmanuel Breuillard·Koji Fujiwara
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Abstract

We recast the notion of joint spectral radius in the setting of groups acting by isometries on non-positively curved spaces and give geometric versions of results of Berger-Wang and Bochi valid for $δ$-hyperbolic spaces and for symmetric spaces of non-compact type. This method produces nice hyperbolic elements in many classical geometric settings. Applications to uniform growth are given, in particular a new proof and a generalization of a theorem of Besson-Courtois-Gallot.

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Emmanuel Breuillard, Koji Fujiwara. 2018-04-02. On the joint spectral radius for isometries of non-positively curved spaces and uniform growth. https://arxiv.org/abs/1804.00748

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