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We study the geodesic flow of geometrically finite quotients$\Omega/{\Gamma}$ of Hilbert geometries, in particular its recurrenceproperties. We prove that, under a geometrical assumption on the cusps, thegeodesic flow is uniformly hyperbolic. Without this assumption, we provide anexample of a quotient whose geodesic flow has a zero Lyapunov exponent. We makethe link between the dynamics of the geodesic flow and some properties of theconvex set $\Omega$ and the group $\Gamma$. As a consequence, we get variousrigidity results which extend previous results of Benoist and Guichard forcompact quotients. Finally, we study the link between volume entropy andcritical exponent; for example, we show that they coincide provided thequotient has finite volume.

Le flot g\'eod\'esique des quotients geometriquement finis des g\'eom\'etries de Hilbert