Geodesic
On the linearization of automorphisms of a~real analytic hypersurface
Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 53-84

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It is proved that relative to certain normal coordinates any local automorphism of a nonspherical real-analytic hypersurface in $\mathbf C^3$ is a fractional-linear transformation. For a hypersurface in $\mathbf C^n$ a system of normal coordinates is constructed relative to which the entire stability group consists only of fractional-linear transformations. Bibliography: 13 titles. 
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     title = {On the linearization of automorphisms of a~real analytic hypersurface},
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V. V. Ezhov. On the linearization of automorphisms of a~real analytic hypersurface. Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 53-84. http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a3/