2026-04-17T05:51:13Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4559492025-10-13T07:24:12Zcom_2072_98col_2072_378192

00925njm 22002777a 4500 dc Llibre, Jaume author Valls, Clàudia author 2021 We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = - y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n - 1 when n = 2, 3, 4, 5, and f has only simple zeroes. We also provide some general results on these uniform isochronous centers for all n ≥ 2. All our results have been revised by the program P4; see Chaps. 9 and 10 of Dumortier et al. (UniversiText, Springer-Verlag, New York, 2006). Polynomial vector field Uniform isochronous center Phase portrait Poincaré disc Phase portraits of uniform isochronous centers with homogeneous nonlinearities