论文标题
在三角偏斜上，非理性圆形旋转
On trigonometric skew-products over irrational circle-rotations
论文作者
论文摘要
我们描述了三角偏度产物图的一些渐近特性在圆的非理性旋转上。限制使用重归于。此处考虑的地图是与能量零的自动双霍夫斯塔特汉密尔顿人有关的。它们类似于几乎是Mathieu地图，但这些因素是通勤的。这使我们能够在重新归一化的情况下构建周期性轨道，对于每个二次非理性，并证明由Hofstadter模型引起的地图对被吸引到这些周期轨道上。人们认为类似的结果对于几乎是Mathieu地图而言是正确的，但目前似乎无法触及。
We describe some asymptotic properties of trigonometric skew-product maps over irrational rotations of the circle. The limits are controlled using renormalization. The maps considered here arise in connection with the self-dual Hofstadter Hamiltonian at energy zero. They are analogous to the almost Mathieu maps, but the factors commute. This allows us to construct periodic orbits under renormalization, for every quadratic irrational, and to prove that the map-pairs arising from the Hofstadter model are attracted to these periodic orbits. Analogous results are believed to be true for the self-dual almost Mathieu maps, but they seem presently beyond reach.
