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Classification of singularities of smooth functions with a finite cyclic symmetry groupстатья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Kudryavtseva Elena Alexandrovna, Onufrienko Maria Victorovna
- Журнал: Russian Journal of Mathematical Physics
- Том: 30
- Номер: 1
- Год издания: 2023
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 76
- Последняя страница: 94
- DOI: 10.1134/S1061920823010053
- Аннотация: The paper studies singularities of smooth functions in two variables invariant under the action of a finite group G by rotations. A classification of critical points appearing in typical parametric families of G-invariant smooth functions with at most two parameters is obtained, when |G| is different from 4. A criterion for reducibility of a smooth G-invariant function to a normal form is obtained, provided that the Taylor polynomial of degree |G| of the function is not a polynomial in x^2+y^2 and the Milnor G-multiplicity (respectively, G-codimension) of the singularity is less than |G| (respectively, |G|/2). A criterion for reducibility of a smooth parametric family of G-invariant functions to a normal from near a critical point of such type is obtained. The criteria are given in terms of partial derivatives of the function at the critical point.
- Добавил в систему: Кудрявцева Елена Александровна