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Abstract. We describe the attracting basins of the origin in [double-struck C]k+1 for the polynomial lifts of Lattès examples. We show that the boundary of these bounded pseudoconvex domains is a quotient of a compact spherical hypersurface, and we describe the singularities that appear. These domains are surprising, because they are very close to the ball, and admit non injective proper holomorphic self-maps. We also explicit some Lattès examples in dimension 2. [ABSTRACT FROM AUTHOR]