2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100823Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We also describe some other, rather special, deformations when $G=SO(1,n)$ and provide a simple proof that any action of a compact Lie group is locally rigid.Slight revision. A few clarifications made, one reference addedDynamical SystemsDifferential Geometry37C85 53C24text