TY - JOUR
T1 - Characterization of the Riccati and Abel Polynomial Differential Systems Having Invariant Algebraic Curves
AU - Giné, Jaume
AU - Llibre, Jaume
N1 - Publisher Copyright:
© 2024 World Scientific Publishing Company.
PY - 2024/4
Y1 - 2024/4
N2 - The Riccati polynomial differential systems are differential systems of the form x' = c 0(x), y' = b 0(x) + b1(x)y + b2(x)y2, where c0 and bi for i = 0, 1, 2 are polynomial functions. We characterize all the Riccati polynomial differential systems having an invariant algebraic curve. We show that the coefficients of the first four highest degree terms of the polynomial in the variable y defining the invariant algebraic curve determine completely the Riccati differential system. A similar result is obtained for any Abel polynomial differential system.
AB - The Riccati polynomial differential systems are differential systems of the form x' = c 0(x), y' = b 0(x) + b1(x)y + b2(x)y2, where c0 and bi for i = 0, 1, 2 are polynomial functions. We characterize all the Riccati polynomial differential systems having an invariant algebraic curve. We show that the coefficients of the first four highest degree terms of the polynomial in the variable y defining the invariant algebraic curve determine completely the Riccati differential system. A similar result is obtained for any Abel polynomial differential system.
KW - Riccati and Abel differential systems
KW - Invariant algebraic curve
KW - First integrals
UR - http://www.scopus.com/inward/record.url?scp=85190557341&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/f2f1839d-2b1b-307f-8940-a311db8fcf45/
U2 - 10.1142/S0218127424500664
DO - 10.1142/S0218127424500664
M3 - Article
SN - 0218-1274
VL - 34
SP - 2450066:1-2450066:7
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 5
M1 - 2450066
ER -