论文标题
平滑动力学扰动的旋转数
Rotation numbers of perturbations of smooth dynamics
论文作者
论文摘要
我们展示了线性循环的小扰动如何具有与基本动力学a的不变度量相关的相对旋转编号，其$ 2 $维二维的捆绑包的最优质的分裂（前提是保留了一些方向）。同样，差异性的小扰动也具有与双曲线集中支持的不变度度量相关的相对旋转数，并且具有上述$ 2 $维的束。 该相对旋转数的性质允许在复杂特征值和更高的规律性中迈向二分法的一些步骤。我们还证明，在有限型类型的瞬时子迁移（实际上高于无限的因素上方）上方的通用平滑线性共同体接纳了一个具有简单Lyapunov Spectrum的周期点。
We show how the small perturbations of a linear cocycle have a relative rotation number associated with an invariant measure of the base dynamics an with a $2$-dimensional bundle of the finest dominated splitting (provided that some orientation is preserved). Likewise small perturbations of diffeomorphisms have a relative rotation number associated with an invariant measure supported in a hyperbolic set and with a $2$-dimensional bundle as above. The properties of that relative rotation number allow some steps towards dichotomies between complex eigenvalues and dominated splittings in higher dimensions and higher regularity. We also prove that generic smooth linear cocycles above a full-shift (and actually above infinite factors of transitive subshift of finite type) admit a periodic point with simple Lyapunov spectrum.
