Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $\mathcal{A}_{\alpha}\left(M\right)$ for arbitrary Liouvillean number $\alpha$

We show that on any smooth compact connected manifold of dimension $m \geq 2$ admitting a smooth non-trivial circle action $ $S$ = \left{S_t\right}{t \in $R$ } $,$ S{t+1}=S_t $, t h e s e t o f w e a k l y m i x i n g$ C^{\infty} $- d i f f e o m o r p h i s m s w h i c h p r e s e r v e b o t h a s m o o t h v o l u m e$ \nu$ and a measurable Riemannian metric is dense in $ $A$ {\alpha} \left(M\right)= \overline{ \left{h \circ S{\alpha} \circ h^{-1} : h \in $Diff$ ^{\infty}\left(M, \nu\right) \right}}^{C^{\infty}}$ for every Liouvillean number $α$ . The proof is based on a quantitative version of the Anosov-Katok-method with explicitly constructed conjugation maps and partitions.

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $A_{α} (M)$ for arbitrary Liouvillean number $α$

文献摘要

讨论

讲解博客

AI智能校验

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $A_{α} (M)$ for arbitrary Liouvillean number $α$

文献摘要

讨论

讲解博客

AI智能校验

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in Aα(M)Aα​(M) for arbitrary Liouvillean number αα

文献摘要

讨论

|讲解博客

|AI智能校验

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in Aα(M)Aα​(M) for arbitrary Liouvillean number αα

文献摘要

讨论

|讲解博客

|AI智能校验

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $A_{α} (M)$ for arbitrary Liouvillean number $α$

讲解博客

AI智能校验

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $A_{α} (M)$ for arbitrary Liouvillean number $α$

讲解博客

AI智能校验