Smooth invariant curves of singularities of vector fields on \({\mathbb{R}}^ 3\) (Q1079258)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Smooth invariant curves of singularities of vector fields on \({\mathbb{R}}^ 3\) |
scientific article; zbMATH DE number 3962805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Smooth invariant curves of singularities of vector fields on \({\mathbb{R}}^ 3\) |
scientific article; zbMATH DE number 3962805 |
Statements
Smooth invariant curves of singularities of vector fields on \({\mathbb{R}}^ 3\) (English)
0 references
1986
0 references
In this paper some aspects of the theory of singularities of vector fields are studied. The main result may be described as follows. Let X be a germ in \(OE{\mathbb{R}}^ 3\) of a \(C^{\infty}\) vector field and D a direction in \({\mathbb{R}}^ 3\). Then there exists a cone of finite contact around D provided that X is not infinitely flat along D. Situations in which such cones exist are analyzed. The blowing up method for singularities of vector fields is extensively used.
0 references
invariant manifold
0 references
theory of singularities of vector fields
0 references
0.9229992
0 references
0 references
0.8949902
0 references
0.8887491
0 references
