具有次线性扩散的环面的保面积无旋同态
Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion
摘要：
我们构造了二维环面的一个$C^\infty$保面积的自同构，该环面关于勒贝格测度是Bernoulli的（特别是遍历的），同伦于恒等式，并且具有到其旋转集为$\{(0,0)\}$的泛覆盖的提升，此外还具有几乎每个提升动力学的轨道都是无界的并且在无穷远的圆的每个方向上积累的性质。
英文摘要：
We construct a $C^\infty$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose rotation set is $\{(0,0)\}$, which in addition has the property that almost every orbit by the lifted dynamics is unbounded and accumulates in every direction of the circle at infinity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
