Nonwandering, nonrecurrent Fatou components in P²

Brendan J. Weickert

Vol. 211 (2003), No. 2, 391–397

DOI: 10.2140/pjm.2003.211.391

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.

Milestones

Received: 17 September 2002

Published: 1 October 2003