Topological obstructions to smoothness for infinitely renormalizable maps of the disc
Topological obstructions to smoothness for infinitely renormalizable maps of the disc
复制标题
无限可重整化的圆盘映射的拓扑障碍
DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
F. Moreira
中科院分区：
文献类型：
--
作者：
F. Moreira
我们分析的签名类型的级联周期轨道与周期加倍重整化映射的二维光盘。签名是一个有理数序列不变的方向保持拓扑共轭，它描述了周期轨道是如何相互联系的。证明了在面积收缩映射类中，签名不可能是单调序列。这就解释了为什么Bowen，Franks和Young的无限可重整映射的经典例子不能用光滑耗散映射来实现，这表明在面积收缩的情况下实现无限可重整映射存在拓扑障碍。
We analyse the signature type of a cascade of periodic orbits associated with period-doubling renormalizable maps of the two-dimensional disc. The signature is a sequence of rational numbers invariant with respect to orientation-preserving topological conjugacies, which describes how periodic orbits are linked around each other. We prove that in the class of area-contracting maps the signature cannot be a monotone sequence. This explains why classical examples of infinitely renormalizable maps due to Bowen, Franks and Young cannot be achieved by smooth dissipative maps, which shows that there are topological obstructions to realizing infinitely renormalizable maps in the area-contracting case.