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On the joint spectral radius for isometries of non-positively curved spaces and uniform growth
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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 $\delta$-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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Cited by 1 Pith paper
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Hierarchically hyperbolic groups and uniform exponential growth
A virtually torsion-free hierarchically hyperbolic group either has uniform exponential growth or its Cayley graph is quasi-isometric to Z times a space.
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