Let f be a holomorphic map of the complex projective space P~n of dimension n onto itself. We assume that f is of degree d ≥ 2. As in the one-dimensional case, the Fatou set Ω for f is defined byrnΩ := {p ∈ P~n {f~j}_(j≥0) is a normal family on a neighborhood of p}.rnIt is sometimes useful to consider the normality of the sequence {f~j]_(j≥0) when restricted to local analytic sets of lower dimension. We introduce a slightly more general concept as follows.
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