Geodesic
Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces
Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 531-552

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Suppose given a smooth strictly pseudoconvex hypersurface not equivalent to the sphere, a point on the surface, and a neighborhood of the point. It is shown that all local automorphisms of the surface defined in an arbitrary neighborhood of a fixed point can be linearized by a suitable choice of local coordinates. It is also shown that given two convergent sequences of real analytic nonspherical hypersurfaces it is possible to extract a convergent subsequence from any sequence of mappings between them. Bibliography: 20 titles. 
@article{IM2_1986_26_3_a3,
     author = {N. G. Kruzhilin},
     title = {Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces},
     journal = {Izvestiya. Mathematics },
     pages = {531--552},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a3/}
}
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N. G. Kruzhilin. Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces. Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 531-552. http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a3/