论文标题
通用性，但没有刚性的二维扰动的刚性
Universality but no rigidity for two-dimensional perturbations of almost commuting pairs
论文作者
论文摘要
在本文中，我们考虑了环的二维耗散图，这是一维临界圆图的小扰动。早些时候，这种扰动允许一种吸引子，该吸引子是一个非平滑的上侧圆圈 - 一个“关键”圆圈。我们研究地图的结合，这些地图承认吸引者并表明，尽管地图表现出了普遍性 - 当观察小尺度时，它们接近某种正常形式 - 通常，两个地图在其关键吸引子上无法平稳地夸张。该结果扩大了A. de Carvalho，M。Lyubich，M。Martens发现的“普遍性但没有刚度”的范式，并扩展到了另一类的动态系统。
In this paper we consider two-dimensional dissipative maps of the annulus which are small perturbations of one-dimensional critical circle maps. It has been shown earlier that such perturbations admit an attractor which is a non-smooth topolgical circle - a "critical" circle. We study conjugacies of the maps that admit such attractors and show that although the maps exhibit universality - they approach a certain normal form when looked at small scales - two maps in general can not be smoothly comjugate on their critical attractors. This result extends the paradigm of "universality but no rigidity" in two dimensions, discovered by A. De Carvalho, M. Lyubich, M. Martens, to yet another class of dynamical systems.
