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This note illustrates the strategy of our paper on piecewise affine surfacehomeomorphisms by giving a new proof of the finite multiplicity of the maximumentropy measure of Anosov diffeomorphisms (here on surfaces). This approachavoids the explicit construction of Markov partitions and will be appliedelsewhere to some non-uniformly hyperbolic diffeomorphisms.

Une nouvelle analyse des mesures maximisant l'entropie des diff\'eomorphismes d'Anosov de surfaces