论文标题
$ c^2 $空间以下的周期三倍和quintupling重量化
Period tripling and quintupling renormalizations below $C^2$ space
论文作者
论文摘要
在本文中，我们探讨了以下$ c^2 $单峰地图的时期三倍和Quintupling重量化。我们表明，对于给定的适当缩放数据，存在着无限额定范围的片段仿射图空间上的重归其化固定点。此外，我们表明，考虑到周期三倍和周期Quintupling Comminatorics，该重归其化固定点扩展到$ C^{1+LIP} $ Un -Imodal地图。此外，我们表明，通过考虑缩放数据的较小变化，存在重新量量化的固定点的连续性。最后，这导致了这样一个事实，即作用于$ c^{1+lip} $单峰地图的三倍和quintupling恢复量像具有无限的拓扑熵。
In this paper, we explore the period tripling and period quintupling renormalizations below $C^2$ class of unimodal maps. We show that for a given proper scaling data there exists a renormalization fixed point on the space of piece-wise affine maps which are infinitely renormalizable. Furthermore, we show that this renormalization fixed point is extended to a $C^{1+Lip}$ unimodal map, considering the period tripling and period quintupling combinatorics. Moreover, we show that there exists a continuum of fixed points of renormalizations by considering a small variation on the scaling data. Finally, this leads to the fact that the tripling and quintupling renormalizations acting on the space of $C^{1+Lip}$ unimodal maps have unbounded topological entropy.
