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) 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, BrasilKeywords: Moduli, Lipschitz equivalence, Hölder equivalence, right equivalence of functions.
In this article, we show the Hölder invariance of the Henry–Parusiński invariant. For a single germ
ƒ, the Henry–Parusiński invariant of ƒ is given in terms of the leading coefficients of the asymptotic expansion of ƒ along the branches of the generic polar curve of ƒ. As a consequence, we obtain that the classification problem of polynomial function-germs, with uniformly bounded degree, under Hölder equivalence, admits moduli.