Résumé
Pacific J. Math., 245 (2010), 201-225 It is shown that the volume entropy of a Hilbert geometry associated to an$n$ -dimensional convex body of class$C^{1,1}$equals$n-1$ . To achieve this result, a new projective invariant of convex bodies, similar to the centro-affine area, is constructed. In the case$n=2$ , and without any assumption on the boundary, it is shown that the entropy is bounded above by$\frac{2}{3-d} \leq 1$ , where$d$is the Minkowski dimension of the extremal set of$K$ . An example of a plane Hilbert geometry with entropy strictly between 0 and 1 is constructed.