TY - JOUR
T1 - Invariant hyperplanes and Darboux integrability for d -dimensional polynomial differential systems
AU - Llibre, Jaume
AU - Rodríguez, Gerardo
PY - 2000/1/1
Y1 - 2000/1/1
N2 - For a class of polynomial differential systems of degree (m1,...,md) in Rd which is open and dense in the set of all polynomial differential systems of degree (m1,...,md) in Rd, we study the maximal number of invariant hyperplanes. This is a well known problem in dimension d=2 (see for instance [1,12,16]). Furthermore, using the Darboux theory of integrability we analyse when can be possible to find a first integral of a polynomial vector field of degree (m1,...,md) in Rd by knowing the existence of a sufficient number of invariant hyperplanes. © 2000 Elsevier, Paris.
AB - For a class of polynomial differential systems of degree (m1,...,md) in Rd which is open and dense in the set of all polynomial differential systems of degree (m1,...,md) in Rd, we study the maximal number of invariant hyperplanes. This is a well known problem in dimension d=2 (see for instance [1,12,16]). Furthermore, using the Darboux theory of integrability we analyse when can be possible to find a first integral of a polynomial vector field of degree (m1,...,md) in Rd by knowing the existence of a sufficient number of invariant hyperplanes. © 2000 Elsevier, Paris.
KW - 34C05
KW - 58F14
KW - 58F22
KW - Darboux integrability
KW - Invariant hyperplane
KW - Polynomial differential system
UR - https://www.scopus.com/pages/publications/0034366260
U2 - 10.1016/S0007-4497(00)01061-7
DO - 10.1016/S0007-4497(00)01061-7
M3 - Article
SN - 0007-4497
VL - 124
SP - 599
EP - 619
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
ER -