Hölder invariance of the Henry-Parusinski invariant

In this article, we show the Hölder invariance of the Henry-Parusinski invariant. For a single germ $f$, the Henry-Parusinski invariant of $f$ is given in terms of the leading coefficients of the asymptotic expansion of $f$ along the branches of the generic polar curve of $f$. As a consequence, we obtain that the classification problem of polynomial function-germs, with uniformly bounded degree, under Hölder equivalence, admits continuous moduli.