Abstract
The following problem is discussed in the paper: What can be assumed by the values dimension of the stabilizer of a point in the Lie algebra of infinitesimal holomorphic symmetries of an arbitrary germ of a real analytic hypersurface in the space C 2? When answering this question, the main difficulty is caused by germs of Cohn’s infinite type that are spherical at the point in general position. The case of hypersurfaces of the form Γ(r) = {υ = ur(|z|2)} is studied completely. There the dimensions of the Lie algebra and its stabilizer can take the values (5,5), (4,2), (3,3), and (2,2). The four classes are described explicitly, and the first three of them are given by elementary functions; the description of these classes involves the rational function Q n (t) = tan(n arctan(t)) similar to the famous Chebyshev polynomial.
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