MOSCOW MATHEMATICAL JOURNAL VOLUME 26, ISSUE 2, APRIL–JUNE 2026Authors: Alexandre Fernandes (1), José Edson Sampaio (1), and Joserlan Perote da Silva (2)Author Institution: (1) Department of Mathematics, Federal University of Ceará, Av. Humberto Monte, s/n Campus do Pici — Block 914, 60455-760 Fortaleza-CE, Brazil (2) Department of Mathematics, University of International Integration of Afro-Brazilian Lusophony (UNILAB), Palmares Campus, Zip Code 62785-000. Acarape-Ce, BrazilKeywords: Moduli, Lipschitz equivalence, Hölder equivalence, right equivalence of functions.
In this article, we demonstrate the Hölder invariance of the Henry–Parusiński invariant. For a single germ $f$, the Henry–Parusiński 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 $f$. Consequently, we show that the classification problem of polynomial function germs, with uniformly bounded degree, under Hölder equivalence admits moduli.
