Large entropy measures of polynomial-like maps

Large entropy measures of endomorphisms were studied by Dinh-Sibony and De Thélin. In particular, they proved that such measures are supported on the Julia set of the endomorphism. In this talk, after introducing the necessary notions, we present a study of large entropy measures in the context of polynomial-like maps. In particular, we show that large entropy measures are supported on the Julia sets of polynomial-like maps. To prove this, we use a different method than the one used by De Thélin and Dinh in the context of endomorphisms.