For convergence groups with expanding coarse-cocycles, the author builds free subsemigroups with critical exponent arbitrarily close to the ambient critical exponent, with applications to transverse groups and Anosov semigroups.
Mesures de Patterson–Sullivan Sur le Bor d d’un Espace Hyperbolique au Sens de Gromov
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Free Semigroups of Large Critical Exponent
For convergence groups with expanding coarse-cocycles, the author builds free subsemigroups with critical exponent arbitrarily close to the ambient critical exponent, with applications to transverse groups and Anosov semigroups.