Recent zbMATH articles in MSC 32Bhttps://zbmath.org/atom/cc/32B2023-11-13T18:48:18.785376ZWerkzeugMalgrange division by quasianalytic functionshttps://zbmath.org/1521.320082023-11-13T18:48:18.785376Z"Bierstone, Edward"https://zbmath.org/authors/?q=ai:bierstone.edward"Milman, Pierre D."https://zbmath.org/authors/?q=ai:milman.pierre-dSummary: Quasianalytic classes are classes of \(\mathcal{C}^\infty\) functions that satisfy the analytic continuation property enjoyed by analytic functions. Two general examples are quasianalytic Denjoy-Carleman classes (of origin in the analysis of linear partial differential equations) and the class of \(\mathcal{C}^\infty\) functions that are definable in a polynomially bounded o-minimal structure (of origin in model theory). We prove a generalization to quasianalytic functions of Malgrange's celebrated theorem on the division of \(\mathcal{C}^\infty\) by real-analytic functions.Analytic moduli for parabolic Dulac germshttps://zbmath.org/1521.370462023-11-13T18:48:18.785376Z"Mardešić, P."https://zbmath.org/authors/?q=ai:mardesic.pavao"Resman, M."https://zbmath.org/authors/?q=ai:resman.majaSummary: This paper gives moduli of analytic classification for parabolic \textit{Dulac} germs (that is, \textit{almost regular} germs). Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of \textit{Écalle-Voronin}-type germs of analytic diffeomorphisms. The result is stated in a broader class of \textit{parabolic generalized Dulac germs} having power-logarithmic asymptotic expansions.