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We discuss the problem of classifying all local CR diffeomorphisms of astrictly pseudoconvex surface. Our method exploits the Tanaka--Websterpseudohermitian invariants, their transformation formulae, and the Chern--Moserinvariants. Our main application concerns a class of generalized ellipsoidswhere we classify all local CR mappings.

Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids