Abstract
AbstractLetf:X→Xbe the restriction to a hyperbolic basic set of a smooth diffeomorphism. We show that in the class ofCr(r>0) cocycles with fiber the special Euclidean group SE(n), those that are transitive form a residual set (countable intersection of open dense sets). This result is new for odd values ofn≥3. More generally, we consider Euclidean-type groupsG⋉ℝnwhereGis a compact connected Lie group acting linearly on ℝn. When Fix G={0}, it is again the case that the transitive cocycles are residual. When Fix G≠{0}, the same result holds upon restriction to the subset of cocycles that avoid an obvious and explicit obstruction to transitivity.
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