发表机构
School of Mathematics and Statistics, Zhengzhou University（郑州大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明对称Fibonacci双峰映射在临界阶足够大时，其临界点的公共ω-极限集为野生Cantor吸引子，并通过半共轭将问题简化为Fibonacci盒映射。
AI 中文摘要
我们考虑具有Fibonacci组合学的光滑对称双峰映射。我们证明，当临界阶足够大时，两个临界点的公共ω-极限集是一个野生Cantor吸引子。利用全族论证，我们首先证明存在具有任意给定临界阶ℓ>3的光滑对称Fibonacci双峰映射。野生吸引子存在性的证明基于一个二对一的半共轭，它将双峰映射的广义重整化简化为具有一个临界点的Fibonacci盒映射。
英文摘要
We consider smooth symmetric bimodal maps with Fibonacci combinatorics. We prove that, when the critical order is sufficiently large, the common $ω$-limit set of the two critical points is a wild Cantor attractor. Using a full-family argument, we first prove the existence of smooth symmetric Fibonacci bimodal maps with any prescribed critical order $\ell>3$. The proof of the existence of the wild attractor is based on a two-to-one semi-conjugacy which reduces the generalized renormalization of the bimodal map to a Fibonacci box mapping with one critical point.
