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We examine the Polish group $H_{+}^{AC}$ of order-preservingself-homeomorphisms $f$ of the interval $\left[ 0,1 \right]$ for which both $f$and $f^{-1}$ are absolutely continuous; in particular, we establish tworesults. First, we prove that $H_{+}^{AC}$ is topologically $2$-generated; infact, it is generically $2$-generated, i.e., there is a dense $G_{\delta}$ setof pairs $\left( f,g \right) \in H_{+}^{AC} \times H_{+}^{AC}$ for which$\left\langle f,g \right\rangle$ is dense. Secondly, we prove that $H_{+}^{AC}$admits a dense $G_{\delta}$ conjugacy class, and we explicitly characterize theelements thereof.

Generation and genericity of the group of absolutely continuous homeomorphisms of the interval