# On a family of mild functions

30 Jun 2020 Van Hille Siegfried

We prove that the function $P_\alpha(x) = \exp(1-x^{-\alpha})$ with $\alpha > 0$, is $1/\alpha$-mild. We apply this result to obtain a uniform $1/\alpha$-mild parametrization of the family of curves $\{xy = \epsilon^2 \mid (x,y) \in (0,1)^2\}$ for $\epsilon \in (0,1)$, which does not have a uniform $0$-mild parametrization by work of Yomdin... (read more)

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# Categories

• NUMBER THEORY
• COMPLEX VARIABLES