Let f be a holomorphic self-map of the unit ball in dimension 2, which does not have an interior fixed point. Suppose that f has a Wolff point p with the boundary dilatation coefficient equal to 1 and the non-tangential differential dfp = id. The local behaviours of f near p are quite diverse, and we give a detailed study in many typical cases. As a byproduct, we give a dynamical interpretation of the Burns–Krantz rigidity theorem. Note also that similar results hold on two-dimensional contractible smoothly bounded strongly pseudoconvex domains.

中文翻译：

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球上沃尔夫点附近的当地研究

让F是第二维单位球的全纯自映射，它没有内部不动点。假设F有一个沃尔夫点p边界膨胀系数等于 1，非切向微分 dFp=ID. 当地人的行为F靠近p种类繁多，我们在许多典型案例中进行了详细研究。作为副产品，我们对 Burns-Krantz 刚性定理进行了动态解释。还要注意，类似的结果适用于二维可收缩平滑有界的强伪凸域。