Computations and ML for surjective rational maps

The present note studies surjective rational endomorphisms f: mathbbP2 dashrightarrow mathbbP2 with cubic terms and the indeterminacy locus If ne emptyset. We develop an experimental approach, based on some Python programming and Machine Learning, towards the classification of such maps; a couple of new explicit f is constructed in this way. We also prove (via pure projective geometry) that a general non-regular cubic endomorphism f of mathbbP2 is surjective if and only if the set If has cardinality at least 3.