$C^2$空间下的三倍和五倍周期重整化
Period tripling and quintupling renormalizations below $C^2$ space
摘要：
本文研究了$C^2$类单峰映射的三倍周期重整化和五倍周期重整化。证明了对于给定的适当尺度数据，在可无限重正化的分段仿射映射空间上存在重正化不动点。此外，我们证明了这个重整化不动点被推广到一个$C^{1+Lip}$单峰映射，考虑周期三倍和周期五倍组合。此外，我们证明了存在一个连续的不动点的重整化通过考虑一个小的变化的标度数据。最后，这导致了作用在$C^{1+Lip}$单峰映射空间上的三重和五重整化具有无界的拓扑熵。
英文摘要：
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.
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