论文标题
定量统计稳定性和对圆的非理性旋转和差异性的线性响应
Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle
论文作者
论文摘要
我们证明了一类小型$ c^{0} $具有非理性旋转数的圆形差异性的小$ c^{0} $扰动的定量统计稳定性结果。我们表明，如果旋转数为二芬太汀，则在地图的扰动下，不变的度量以Hölder的方式变化，而Hölder指数取决于旋转数的二苯胺类型。一组可允许的扰动包括来自空间离散化的扰动，因此包括数值截断。我们还显示了线性响应，用于平滑扰动，以保留旋转数以及更多一般的扰动。这是从KAM理论中完成的{通过}经典工具完成的，而定量稳定性结果是通过应用于具有弱拓扑的合适度量空间的转移操作员技术获得的。
We prove quantitative statistical stability results for a large class of small $C^{0}$ perturbations of circle diffeomorphisms with irrational rotation numbers. We show that if the rotation number is Diophantine the invariant measure varies in a Hölder way under perturbation of the map and the Hölder exponent depends on the Diophantine type of the rotation number. The set of admissable perturbations includes the ones coming from spatial discretization and hence numerical truncation. We also show linear response for smooth perturbations that preserve the rotation number, as well as for more general ones. This is done {by means of} classical tools from KAM theory, while the quantitative stability results are obtained by transfer operator techniques applied to suitable spaces of measures with a weak topology.
