Abstract
We prove a general perturbation result for smooth Lie group actions with nontrivial finite‐dimensional cohomology. It describes sufficient conditions on cohomology over an action which imply that the action lies in a finite‐dimensional family of actions such that any small perturbation of the family intersects the smooth conjugacy class of the given action. We cast the classical KAM result on perturbations of Diophantine vector fields on tori into this general setup, and we address a few applications and potential applications of this result to homogeneous Lie group actions with finite‐dimensional first cohomology. © 2014 Wiley Periodicals, Inc.
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