68170

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Smooth Local Normal Forms of Hyperbolic Roussarie Vector Fields

ISBN/ISSN: 

1609-3321

DOI: 

10.17323/1609-4514-2021-21-2-413-426

Наименование источника: 

  • Moscow Mathematical Journal

Обозначение и номер тома: 

Т. 21, вып. 2

Город: 

  • Moscow

Издательство: 

  • Independent University of Moscow

Год издания: 

2021

Страницы: 

413-426
Аннотация
In 1975, Roussarie studied a special class of vector fields, whose singular points fill a submanifold of codimension two and the ratio between two non-zero eigenvalues $\lambda_1:\lambda_2=1:-1$. He established a smooth orbital normal form for such fields at points where $\lambda_{1,2}$ are real and the quadratic part of the field satisfied a certain genericity condition. In this paper, we establish smooth orbital normal forms for such fields at points where this condition fails. Moreover, we prove similar results for vector fields, whose singular points fill a submanifold of codimension two and the ratio between two non-zero eigenvalues $\lambda_1:\lambda_2=p:-q$ with arbitrary integers $p,q \ge 1$.

Библиографическая ссылка: 

Павлова Н.Г., Ремизов А.О. Smooth Local Normal Forms of Hyperbolic Roussarie Vector Fields // Moscow Mathematical Journal. 2021. Т. 21, вып. 2. С. 413-426.