Intrinsic character of Stokes matrices
| Autor: | Christiane Rousseau, Jean-François Gagnon |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis 34M40 34M03 Dynamical Systems (math.DS) 01 natural sciences Projection (linear algebra) 010101 applied mathematics Singularity Character (mathematics) Intersection Line (geometry) FOS: Mathematics Order (group theory) Mathematics - Dynamical Systems 0101 mathematics Rotation (mathematics) Eigenvalues and eigenvectors Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 262(3):2608-2617 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2016.11.019 |
| Popis: | Two germs of linear analytic differential systems $x^{k+1}Y^\prime=A(x)Y$ with a non resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in $S$ allows supposing that $\mathbb R^+$ lies in the intersection of two sectors. Reordering of the coordinates of $Y$ allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in $x$ is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin. 10 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect