Arnold's seminar, October 20, 1998.
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V.I.Arnold.<BR>
Simple curves singularities.
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  Germs of smooth mappings of R or C to R^n or C^n are classified up to the
diffeomorphism of the images. Mappings starting from quadratic or cubical
terms are simple (have no moduli), but for higher degeneracy moduli occur.
The relation to the coartinian algebras and semigroups of integers is
discussed.