论文标题
圆环某些流的奇异总和的对数范围：简短的证明
Logarithmic bounds for ergodic sums of certain flows on the torus: a short proof
论文作者
论文摘要
我们提供了一个简短的证据，表明$ \ Mathcal {C}^1 $可观察到的Ergodic和$ \ MATHCAL {C}^1 $在$ \ Mathbb {T}^2 $上流动的封闭横向曲线，其poincaré地图在大多数差异上都具有稳定的旋转偏差，从而使封闭的横向曲线在linearthmearthmearthyly上具有差异。为此，我们将后者的组成部分与可观察到的圆形可观察到的Birkhoff总和联系起来，并使用Denjoy-Koksma不平等。我们还举例说明了满足上述假设的非最小流动。
We give a short proof that the ergodic sums of $\mathcal{C}^1$ observables for a $\mathcal{C}^1$ flow on $\mathbb{T}^2$ admitting a closed transversal curve whose Poincaré map has constant type rotation number have growth deviating at most logarithmically from a linear one. For this, we relate the latter integral to the Birkhoff sum of a well-chosen observable on the circle and use the Denjoy-Koksma inequality. We also give an example of a nonminimal flow satisfying the above assumptions.
