Abstract

Let Ω be a nonwandering, nonrecurrent Fatou component for a holomorphic self-map f of P² of degree d ≥ 2, and let h be a normal limit of the family of iterates of f. We prove that Σ := h(Ω) is either a fixed point of f or its normalization is a hyperbolic Riemann surface, so that the dynamics of f|_Σ may be lifted to the unit disk. We also show that basins of attraction for holomorphic self-maps of P^k of degree d ≥ 2 are taut.

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