69349

Автор(ы): 

Автор(ов): 

1

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

The Poincaré Index and Its Applications

Электронная публикация: 

Да

ISBN/ISSN: 

2218-1997

DOI: 

10.3390/universe8040223

Наименование источника: 

  • Universe

Обозначение и номер тома: 

Vol. 8, Iss.4

Город: 

  • Basel, Switzerland

Издательство: 

  • MDPI

Год издания: 

2022

Страницы: 

https://www.mdpi.com/2218-1997/8/4/223/htm
Аннотация
We discuss an approach to the problem of calculating the local topological index of vector fields given on complex spaces or varieties with singularities developed by the author over the past few years. Our method is based on the study of the homology of a contravariant version of the classical Poincaré–de Rham complex. This idea allows not only simplifying the calculations, but also clarifying the meaning of the basic constructions underlying many papers on the subject. In particular, in the graded case, the index can be expressed explicitly in terms of the elementary symmetric polynomials. We also considered some useful applications in physics, mechanics, control theory, the theory of bifurcations, etc.

Библиографическая ссылка: 

Александров А.Г. The Poincaré Index and Its Applications // Universe. 2022. Vol. 8, Iss.4. С. https://www.mdpi.com/2218-1997/8/4/223/htm.