On the Lattes maps of Pk
Abstract
Let f be a polynomial endomorphism of degree d>1 of Ck (k>1) which extends to a holomorphic endomorphism of Pk. Assume that the maximal order Julia set of f is laminated by real hypersurfaces in some open set. We show that f is homogenous and is a polynomial lift of a Lattes endomorphism of Pk-1.
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