TY - JOUR
T1 - Phase Portraits of Uniform Isochronous Centers with Homogeneous Nonlinearities
AU - Llibre, Jaume
AU - Valls, Claudia
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
PY - 2022/4
Y1 - 2022/4
N2 - 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).
AB - 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).
KW - Phase portrait
KW - Poincaré disc
KW - Polynomial vector field
KW - Uniform isochronous center
UR - http://www.scopus.com/inward/record.url?scp=85101137275&partnerID=8YFLogxK
U2 - 10.1007/s10883-021-09529-2
DO - 10.1007/s10883-021-09529-2
M3 - Article
AN - SCOPUS:85101137275
SN - 1079-2724
VL - 28
SP - 319
EP - 332
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
IS - 2
ER -