We solve the regularity problem for Milnor's infinite dimensional Lie groups in the asymptotic estimate context. Specifically, let $G$ be a Lie group with asymptotic estimate Lie algebra $\mathfrak{g}$, and denote its evolution map by $\mathrm{evol}\colon \mathrm{D}\equiv \mathrm{dom}[\mathrm{evol}]\rightarrow G$, i.e., $\mathrm{D}\subseteq C^0([0,1],\mathfrak{g})$... (read more)

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