论文标题
严格的计算机辅助界限，在临界点4
Rigorous computer-assisted bounds on the period doubling renormalisation fixed point and eigenfunctions in maps with critical point of degree 4
论文作者
论文摘要
我们在重态度的固定点上获得了严格的严格界限，以在单峰地图的家族中加倍的固定点，该学位$ 4 $关键点。我们使用一个收缩映射参数来绑定基本特征函数和特征值，以实现操作员的线性化和控制添加噪声缩放的操作员。具有严格的定向舍入的多精确算术用于在分析功能的空间中绑定操作，从而在功率系列系数和通用常数上产生紧密的界限，至$ 320 $超过320美元。
We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree $4$ critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for the linearisation of the operator and for the operator controlling the scaling of added noise. Multi-precision arithmetic with rigorous directed rounding is used to bound operations in a space of analytic functions yielding tight bounds on power series coefficients and universal constants to over $320$ significant figures.
