**abstract:**
We shall prove that given $H>0$ and $\delta\geq 0$ there is a finite number (up to isomorphisms) of marked groups $(\Gamma , \Sigma)$ which are$\delta$-hyperbolic, torsion-free, non cyclic such that their entropy satisfies ${\rm Entropy} (\Gamma , \Sigma) \le H$. Here $\Gamma$ is finitely generated and endowed with a (symmetric) finite generating set $\Sigma$. The goal of the talk is to explain all the words in this abstract and give a flavour of the proof.

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