ON THE BOUNDARY ORBIT ACCUMULATION SET FOR A DOMAIN WITH NON-COMPACT AUTOMORPHISM GROUP

ALEXANDER V. ISAEV STEVEN G. KRANTZ

Abstract. For a smoothly bounded pseudoconvex domain D ⊂ ℂ^{n} of finite type with non-compact holomorphic automorphism group Aut(D), we show that the set S(D) of all boundary accumulation points for Aut(D) is a compact subset of ∂D and, if S(D) contains at least three points, it is connected and thus has the power of the continuum. We also discuss how S(D) relates to other invariant subsets of ∂D and show in particular that S(D) is always a subset of the Šilov boundary.