The Poincaré Index and Its Applications

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 Poin...

Full description

Saved in:
Bibliographic Details
Published inUniverse (Basel) Vol. 8; no. 4; p. 223
Main Author Aleksandrov, Alexander G.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2022
Subjects
bifurcations
Control theory
deformations
Dynamical systems
Equilibrium
index theory
logarithmic differential forms
Mathematics
Mechanics
Ordinary differential equations
Physics
singularities
vector fields
Online AccessGet full text
ISSN2218-1997
2218-1997
DOI10.3390/universe8040223

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2218-1997
2218-1997
DOI:10.3390/universe8040223