Typical dynamics of Newton's method

This article consists of two papers: $\mathit{\text{Typical}}\mathit{\text{dynamics}}\mathit{\text{of}}\mathit{\text{Newton’s}}\mathit{\text{method}}$ by Steele and $\mathit{\text{Erratum}}\mathit{\text{to}}\mathit{\text{"Typical}}\mathit{\text{dynamics}}\mathit{\text{of}}\mathit{\text{Newton’s}}\mathit{\text{method"}}$ by Dudák and Steele. Let $C^1(M)$ be the space of continuously differentiable real-valued functions defined on $[-M,M]$. We show that for the typical element $f$ in $C^1(M)$, there exists a set $S\subseteq [-M,M]$, both residual and of full measure in $[-M,M]$, such that for any $x\in S$, the trajectory generated by Newton’s method using $f$ and $x$ either diverges, converges to a root of $f$, or generates a Cantor set as its attractor. Whenever the Cantor set is the attractor, the dynamics on the attractor are described by a single type of adding machine, so that the dynamics on all of these attracting Cantor sets are topologically equivalent.