Hölder classifications of finite-dimensional linear flows
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915594943594496 |
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| author | Berger, Arno Wynne, Anthony |
| author_facet | Berger, Arno Wynne, Anthony |
| contents | Two flows on a finite-dimensional normed space $X$ are equivalent if some homeomorphism $h$ of $X$ preserves all orbits, i.e., $h$ maps each orbit onto an orbit. Under the assumption that $h$, $h^{-1}$ both are $β$-Hölder continuous near the origin for some (or all) $0<β< 1$, a complete classification with respect to some-Hölder (or all-Hölder) equivalence is established for linear flows on $X$, in terms of basic linear algebra properties of their generators. Consistently utilizing equivalence instead of the more restrictive conjugacy, the classification theorems extend and unify known results. Though entirely elementary, the analysis is somewhat intricate and highlights, more clearly than does the existing literature, the fundamental roles played by linearity and the finite-dimensionality of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder classifications of finite-dimensional linear flows Berger, Arno Wynne, Anthony Dynamical Systems Classical Analysis and ODEs Two flows on a finite-dimensional normed space $X$ are equivalent if some homeomorphism $h$ of $X$ preserves all orbits, i.e., $h$ maps each orbit onto an orbit. Under the assumption that $h$, $h^{-1}$ both are $β$-Hölder continuous near the origin for some (or all) $0<β< 1$, a complete classification with respect to some-Hölder (or all-Hölder) equivalence is established for linear flows on $X$, in terms of basic linear algebra properties of their generators. Consistently utilizing equivalence instead of the more restrictive conjugacy, the classification theorems extend and unify known results. Though entirely elementary, the analysis is somewhat intricate and highlights, more clearly than does the existing literature, the fundamental roles played by linearity and the finite-dimensionality of $X$. |
| title | Hölder classifications of finite-dimensional linear flows |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2511.02001 |