论文标题
某些偏斜图的通用超临界行为
Universal supercritical behavior for some skew-product maps
论文作者
论文摘要
我们考虑偏斜的旋转图$ x \ mapsto x+α$（mod 1），其因子在sl（2，r）中取值的因素在数值实验中具有$α$的金色平均值，斐波那契的纤维含量，几乎是MATHIEU图，几乎具有旋转$ 1/4 $ 1/4 $ lyapunov enapunov Exportion cancortic scaritiate scaring As-ymptotic scaring scaping scaping scaping acting scaport actrant acting As-yptotity scaring scaping scaring sucting Asmptitic scaring。我们证明了对于“周期性”旋转数字和大型Lyapunov指数的存在的渐近缩放。这种现象是普遍的，从某种意义上说，它适用于开放的地图集，其缩放限量与地图无关。具有定期旋转编号的一组地图是在合适的地图空间中的真实分析编成$ 1 $歧管。
We consider skew-product maps over circle rotations $x\mapsto x+α$ (mod 1) with factors that take values in SL(2,R) In numerical experiments with $α$ the inverse golden mean, Fibonacci iterates of almost Mathieu maps with rotation number $1/4$ and positive Lyapunov exponent exhibit asymptotic scaling behavior. We prove the existence of such asymptotic scaling for "periodic" rotation numbers and for large Lyapunov exponent. The phenomenon is universal, in the sense that it holds for open sets of maps, with the scaling limit being independent of the maps. The set of maps with a given periodic rotation number is a real analytic codimension $1$ manifold in a suitable space of maps.
