We prove that, if f is a homeomorphism of the 2-torus isotopic to the identity whose rotation set is a non-degenerate segment and f has a periodic point, then it has uniformly bounded deviations in the direction perpendicular to the segment.

中文翻译：

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一类环面同胚不存在次线性扩散

我们证明，如果f是 2-torus 同位素与旋转集是非退化段的恒等式的同胚，并且f具有周期点，则它在垂直于段的方向上具有一致的有界偏差。