Let be a smoothly bounded domain in ރ 2 such that the Bergman representative map near the boundary continues to be diffeomorphic up to the boundary. If such a domain admits a holomorphic automorphism group orbit accumulating at a boundary point of finite D'Angelo type 2m, we show that the domain is biholomorphic to the Thullen domain {(z, w) ∈ ރ 2 : |z| 2m + |w| 2 < 1}. This result refines the well-known theorem of E. Bedford and S. Pinchuk.
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