Article Contents
Article Contents

# Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure

• We describe in detail a construction of weakly mixing $C^\infty$ diffeomorphisms preserving a smooth measure and a measurable Riemannian metric as well as ${\mathbb} Z^k$ actions with similar properties. We construct those as a perturbation of elements of a nontrivial non-transitive circle action. Our construction works on all compact manifolds admitting a nontrivial circle action.
It is shown in the appendix that a Riemannian metric preserved by a weakly mixing diffeomorphism can not be square integrable.
Mathematics Subject Classification: 58F11 (primary), 28D05, 57R50, 53C99 (secondary).

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