Weakly mixing di eomorphisms preserving a measurable Riemannian metric with prescribed Liouvillean rotation behavior
Weakly mixing di eomorphisms preserving a measurable Riemannian metric with prescribed Liouvillean rotation behavior
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弱混合二同态保留了可测量的黎曼度量与规定的刘维尔旋转行为
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Philipp Kunde
中科院分区：
文献类型：
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作者：
Roland Gunesch;Philipp Kunde
我们证明了在任意维数m≥2的光滑紧连通流形上，存在光滑非平凡圆作用S = {St}t∈R, St+1 = St，同时保持光滑体积ν和可测量黎曼度规的弱混合C∞-di同态集合在a α (m) = {h◦Sα◦h−1:h∈Di∞(m,ν)} C∞中是密集的。证明是基于一个定量版本的近似的共轭方法与明确构造的共轭映射和分区。
We show that on any smooth compact connected manifold of dimension m ≥ 2 admitting a smooth non-trivial circle action S = {St}t∈R, St+1 = St, the set of weakly mixing C∞-di eomorphisms which preserve both a smooth volume ν and a measurable Riemannian metric is dense in Aα (M) = {h ◦ Sα ◦ h−1 : h ∈ Di ∞ (M,ν)} C∞ for every Liouvillean number α. The proof is based on a quantitative version of the approximation by conjugationmethod with explicitly constructed conjugation maps and partitions.