Pseudonormal form and finite-smooth equivalence of real autonomous systems with two purely imaginary eigenvalues (Q416957)
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: Pseudonormal form and finite-smooth equivalence of real autonomous systems with two purely imaginary eigenvalues |
scientific article; zbMATH DE number 6032820
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pseudonormal form and finite-smooth equivalence of real autonomous systems with two purely imaginary eigenvalues |
scientific article; zbMATH DE number 6032820 |
Statements
Pseudonormal form and finite-smooth equivalence of real autonomous systems with two purely imaginary eigenvalues (English)
0 references
10 May 2012
0 references
This paper deals with a system of autonomous ODEs of class \(C^{\infty}\) having an equilibrium for which the linearized system has a pair of purely imaginary eigenvalues. By means of weakly degenerate transformations the author brings the system into a pseudo-normal form. This approach makes it possible to solve the problem of local finitely smooth equivalence between a system with two purely imaginary eigenvalues and its reduced form. The methodology is described in several theorems whose proofs are not included.
0 references
pseudo-normal forms
0 references
shearing transformations
0 references
transformations with singularities
0 references
weakly degenerate transformations
0 references
0 references
