This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space \(C ^{1+Lip}\) symmetric bimodal maps. Moreover, we show that the topological entropy of the renormalization operator defined on the space of \(C^{1+Lip}\) symmetric bimodal maps is infinite. Further we prove the existence of a continuum of fixed points of renormalization. Consequently, this proves the non-rigidity of the renormalization of symmetric bimodal maps.

中文翻译：

---

低平滑度的对称双峰图的重新归一化

本文讨论了具有低平滑度的对称双峰图的重归一化。我们证明了空间\（C ^ {1 + Lip} \）对称双峰图中存在重归一化固定点。此外，我们表明在\（C ^ {1 + Lip} \）对称双峰图空间上定义的重归一化算子的拓扑熵是无限的。进一步，我们证明了重归一化的固定点的连续性的存在。因此，这证明了对称双峰图的重新规范化的非刚性。