We extend the one dimensional Denjoy-Sacksteder theorems to some diffeomorphism groups of smooth compact closed n-dimensional manifolds. More precisely, we show the existence of a non trivial stabilizer for actions of “quasi-conformal groups” admitting an “exceptional” minimal set which is of “strongly decreasing type”; our results include the classical Denjoy-Sacksteder theorems.
"Denjoy-Sacksteder theory for groups of diffeomorphisms." J. Math. Soc. Japan 63 (3) 985 - 1000, July, 2011. https://doi.org/10.2969/jmsj/06330985