On the conservative pasting lemma

Abstract

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 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 $C^{r,\alpha }$ ($r\in {\mathbb{Z}}^{+}$, $0<\alpha <1$) and $C^{\infty }$ settings, the resulting diffeomorphism having the same regularity as the original one.

final version, to appear in ETDS; important footnote on page 9

References in corpus (1)

• Dacorogna-Moser theorem on the Jacobian determinant equation with control of support

Cited by in corpus (1)

• Accessibility and centralizers for partially hyperbolic flows