Moscow Mathematical Journal

Volume 26, Issue 2, April–June 2026 pp. 145–161.

Hölder Invariance of the Henry–Parusiński Invariant

Authors: Alexandre Fernandes (1), José Edson Sampaio (1), and Joserlan Perote da Silva (2)
Author institution:(1) Departamento de Matemática, Universidade Federal do Ceará, Av. Humberto Monte, s/n Campus do Pici - Bloco 914, 60455-760 Fortaleza-CE, Brazil
(2) Departamento de Matemática, Universidade de Integração Internacional da Lusofonia Afro-Brasileira (UNILAB), Campus dos Palmares, Cep. 62785-000. Acarape-Ce, Brasil

Summary:

In this article, we show 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 $f$. As a consequence, we obtain that the classification problem of polynomial function-germs, with uniformly bounded degree, under Hölder equivalence, admits moduli.

2020 Math. Subj. Class. 14B05; 32S50.

Keywords: Moduli, Lipschitz equivalence, Hölder equivalence, right equivalence of functions.

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