AI 中文总结
该论文证明了中性二次多项式完全重整化吸引子的组合刚性，即相同组合的重整化塔在母刺猬邻域上共形共轭，涵盖无理组合与抛物富集，并建立中性级联的仿射共轭性。
AI 中文摘要
我们证明了中性二次多项式完全重整化吸引子的组合刚性。更精确地说，任何两个具有相同组合结构的双向无限重整化塔在它们的母刺猬邻域上是共形共轭的。该刚性定理包括任意无理组合结构及相应的抛物富集。证明依赖于对中性级联的全面分析，即由中性二次多项式首次返回映射的重标度极限产生的超越动力系统。我们建立了中性级联的一致蝴蝶界，并证明了任意两个组合等价的中性级联是仿射共轭的。我们还证明了具有等价向后组合结构的抛物塔的刚性。
英文摘要
We prove combinatorial rigidity for the full renormalization attractor of neutral quadratic polynomials. More precisely, any two bi-infinite renormalization towers with the same combinatorics are conformally conjugate on neighborhoods of their Mother Hedgehogs. The rigidity theorem includes arbitrary irrational combinatorics and respective parabolic enrichments. The proof relies on a comprehensive analysis of neutral cascades, i.e. transcendental dynamical systems arising from the rescaled limits of the first return maps of neutral quadratic polynomials. We establish uniform butterfly bounds for neutral cascades and prove that any two combinatorially equivalent neutral cascades are affinely conjugate. We also prove rigidity for parabolic towers with equivalent backward combinatorics.
Comments118 pages, 23 figures
