On Lipschitz equivalence of finite-dimensional linear flows
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908835226058752 |
|---|---|
| author | Berger, Arno Wynne, Anthony |
| author_facet | Berger, Arno Wynne, Anthony |
| contents | Two flows on a finite-dimensional normed space $X$ are Lipschitz equivalent if some homeomorphism $h$ of $X$ that is bi-Lipschitz near the origin preserves all orbits, i.e., $h$ maps each orbit onto an orbit. A complete classification by Lipschitz equivalence is established for all linear flows on $X$, in terms of basic linear algebra properties of their generators. Utilizing equivalence instead of the much more restrictive conjugacy, the classification theorem significantly extends known results. The analysis is entirely elementary though somewhat intricate. It highlights, more clearly than does the existing literature, the fundamental roles played by linearity and finite-dimensionality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Lipschitz equivalence of finite-dimensional linear flows Berger, Arno Wynne, Anthony Dynamical Systems Classical Analysis and ODEs 34A30, 34C41, 34D08, 37C15 Two flows on a finite-dimensional normed space $X$ are Lipschitz equivalent if some homeomorphism $h$ of $X$ that is bi-Lipschitz near the origin preserves all orbits, i.e., $h$ maps each orbit onto an orbit. A complete classification by Lipschitz equivalence is established for all linear flows on $X$, in terms of basic linear algebra properties of their generators. Utilizing equivalence instead of the much more restrictive conjugacy, the classification theorem significantly extends known results. The analysis is entirely elementary though somewhat intricate. It highlights, more clearly than does the existing literature, the fundamental roles played by linearity and finite-dimensionality. |
| title | On Lipschitz equivalence of finite-dimensional linear flows |
| topic | Dynamical Systems Classical Analysis and ODEs 34A30, 34C41, 34D08, 37C15 |
| url | https://arxiv.org/abs/2602.13877 |