Geodesic
Properties of sets of isometries of Gromov hyperbolic spaces
Eduardo Oregón-Reyes1
1Pontificia Universidad Católica de Chile, Santiago, Chile
Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 889-910

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DOI

We prove an inequality concerning isometries of a Gromov hyperbolic metric space, which does not require the space to be proper or geodesic. It involves the joint stable length, a hyperbolic version of the joint spectral radius, and shows that sets of isometries behave like sets of2×2 real matrices. Among the consequences of the inequality, we obtain the continuity of the joint stable length and an analogue of Berger–Wang theorem.
DOI : 10.4171/ggd/468
Classification : 53-XX, 15-XX, 20-XX
Mots-clés : Gromov hyperbolic space, stable length, joint spectral radius

Eduardo Oregón-Reyes  1

1 Pontificia Universidad Católica de Chile, Santiago, Chile 
Eduardo Oregón-Reyes. Properties of sets of isometries of Gromov hyperbolic spaces. Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 889-910. doi: 10.4171/ggd/468
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     title = {Properties of sets of isometries of {Gromov} hyperbolic spaces},
     journal = {Groups, geometry, and dynamics},
     pages = {889--910},
     year = {2018},
     volume = {12},
     number = {3},
     doi = {10.4171/ggd/468},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/468/}
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