论文标题
二次家族的分数敏感性功能：Misiurewicz-Thurston参数
Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters
论文作者
论文摘要
对于二次家族，我们定义了与随机地图上可观察到的C^1相关的分数敏感功能的两变量（$η$和$ z $）。我们还定义了近似“冷冻”的分数敏感性函数。如果参数是误导性的，则表明，如果“半二”横向条件保持，那么冷冻易感函数对于通用可观察物的$ z = 1 $。我们在合适的集合$ω$上介绍了“惠特尼”的分数积分和衍生物。我们根据我们对冷冻易感函数和数值实验的结果支持的猜想。特别是，我们期望$η= 1/2 $的分数敏感性功能在$ z = 1 $中是单数，用于collet-ceckmann地图和通用可观察物。我们将这项工作视为朝着悖论解决的一步，即尽管缺乏线性响应，但Misiurewicz-Thurston Maps的经典易感性功能在$ z = 1 $中是$ z = 1 $。
For the quadratic family, we define the two-variable ($η$ and $z$) fractional susceptibility function associated to a C^1 observable at a stochastic map. We also define an approximate, "frozen" fractional susceptibility function. If the parameter is Misiurewicz-Thurston, we show that the frozen susceptibility function has a pole at $z=1$ for generic observables if a "one-half" transversality condition holds. We introduce "Whitney" fractional integrals and derivatives on suitable sets $Ω$. We formulate conjectures supported by our results on the frozen susceptibility function and numerical experiments. In particular, we expect that the fractional susceptibility function for $η=1/2$ is singular at $z=1$ for Collet-Eckmann maps and generic observables. We view this work as a step towards the resolution of the paradox that the classical susceptibility function is holomorphic at $z=1$ for Misiurewicz-Thurston maps, despite lack of linear response.
