We call a local homeomorphism $f: (R^n,0)\to(R^n,0)$ blow-analytic if itbecomes real analytic after composing with a finite number blowings-up withsmooth nowhere dense centers. If the graph of $f$ is semi-algebraic then, by atheorem of Bierstone and Milman, $f$ is blow-analytic if and only if it isarc-analytic: the image by $f$ of a parametrized real analytic arc is again areal analytic arc. For a semialgebraic homeomorphism $f$ we show that if $f$ is blow-analyticand the inverse of $f$ is Lipschitz, then $f$ is Lipschitz and the inverse of$f$ is blow-analytic. The proof is by a motivic integration argument, usingadditive invariants on the spaces of arcs.
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机译：我们称它为局部同胚$ f：（R ^ n，0）\ to（R ^ n，0）$吹动解析，如果它是由有限数量的爆炸所组成，并且没有光滑的密集中心，则成为实解析。如果$ f $的图形是半代数的，那么根据Bierstone和Milman的定理，$ f $是吹动分析的，当且仅当它是arc-analytic时：参数化的真实分析弧的$ f $图像再次出现面分析弧。对于半代数同胚同构$ f $，我们证明了如果$ f $是打击分析的，而$ f $的逆是Lipschitz，则$ f $是Lipschitz，而$ f $的逆是打击分析。证明是根据动机积分论证，在圆弧空间上使用了加性不变量。
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