1 results
On the conservative pasting lemma
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 5 / May 2020
- Published online by Cambridge University Press:
- 17 October 2018, pp. 1402-1440
- Print publication:
- May 2020
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- Article
- Export citation
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Several perturbation tools are established in the volume-preserving setting allowing for the pasting, extension, localized smoothing and local linearization of vector fields. The pasting and the local linearization hold in all classes of regularity ranging from
$C^{1}$ to 
$C^{\infty }$ (Hölder included). For diffeomorphisms, a conservative linearized version of Franks’ lemma is proved in the 
$C^{r,\unicode[STIX]{x1D6FC}}$ (
$r\in \mathbb{Z}^{+}$, 
$0<\unicode[STIX]{x1D6FC}<1$) and 
$C^{\infty }$ settings, the resulting diffeomorphism having the same regularity as the original one.
