Robust local Hölder rigidity of circle maps with breaks
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Bibliographic record
Abstract
We prove that, for every \varepsilon \in (0,1) , every two C^{2 + \alpha } -smooth (\alpha > 0) circle diffeomorphisms with a break point, i.e. circle diffeomorphisms with a single singular point where the derivative has a jump discontinuity, with the same irrational rotation number \rho \in (0,1) and the same size of the break c \in \mathbb{R}_{ + }\backslash \{1\} , are conjugate to each other via a conjugacy which is (1−\varepsilon ) -Hölder continuous at the break points. An analogous result does not hold for circle diffeomorphisms even when they are analytic.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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